I assume you're asked to compute
[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx[/tex]
using both of the substitutions provided.
With [tex]u=x-4[/tex], we have [tex]x=u+4[/tex] and [tex]dx=du[/tex]. Then
[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{30(u+4)^2}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \frac{u^2 + 8u + 16}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \left(u^{3/2} + 8u^{1/2} + 16u^{-1/2}\right) \, du \\\\ ~~~~~~~~ = 30 \left(\frac25 u^{5/2} + \frac{16}3 u^{3/2} + 32 u^{1/2}\right) + C \\\\ ~~~~~~~~ = 12 u^{5/2} + 160 u^{3/2} + 960 u^{1/2} + C \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4 \sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]
With [tex]u=\sqrt{x-4}[/tex], we have
[tex]u^2 = x-4 \implies x^2 = (u^2+4)^2[/tex]
and [tex]2u\,du=dx[/tex]. Then
[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{60u \left(u^2+4\right)^2}u \, du \\\\ ~~~~~~~~ = 60 \int \left(u^4 + 8u^2 + 16\right) \, du \\\\ ~~~~~~~~ = 60 \left(\frac15 u^5 + \frac83 u^3 + 16u\right) + C \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4\sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]
Provide proof for following situation.
look above please to the attachment.
The proof for the side AB congruent to side ED is given below.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
Given that
C is the intersecting point of AD and EB.
Side AC is congruent to side EC.
Also ∠A = ∠E
By vertical angles theorem, a pair of intersecting lines form 2 pairs of vertically opposite angles which are equal.
Therefore, ∠ACB = ∠ECD
Also given that sides AC and EC are congruent.
By ASA congruence theorem, if two angles and an included side of a triangle is equal to the corresponding two angles and included side of another triangle, then the triangles are congruent.
So triangles ABC and CDE are congruent.
C is the common point for both the triangles.
So the side opposite to C are AB and ED.
So they are equal and thus congruent.
Hence the sides AB and ED are proved to be congruent.
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The parallelogram shown on the grid represents a mirror. The mirror hangs on a
wall that is covered with square tiles. Each grid square represents ane tile The side
length of each square tile is 4 in. What is the area of the mirror? Show your work
The area of the mirror is 480 square inches
How to determine the area of the mirrorFrom the question, we have the following parameters that can be used in our computation:
A mirror that has the shape of a parallelogram (see attachment)
From the attachment, we have the following dimensions
Base length = 5 units
Height = 6 units
The area is the product of the dimensions
Since the side length of each square tile is 4 in, then we have
Area = 4 * 4 * 5 * 6
Evaluate
Area = 480
Hence, the area is 480 square inches
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Write an equation of the ellipse with foci (0,+-4) and co-vertices at (±4,0).
When the ellipse has co-vertices at (4,0) and foci at (0,+-4), the equation is y2/32+x2/16=1.
what is equation ?The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
The center is
=(0,0)
The equation is
y2/a2+x2/b2=1
b=4
c=4
a2=b2+c2
=16+16=32
When the ellipse has co-vertices at (4,0) and foci at (0,+-4), the equation is y2/32+x2/16=1.
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Which of the following grids correctly graphs the points A (3, 1), B (0, 3), and C (1, 3)?
A grid that correctly graphs the points A (3, 1), B (0, 3), and C (1, 3) include the following: B. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 3 units to the right and 1 unit above the origin. Point B is plotted 3 units above the origin. Point C is plotted 1 unit to the right and 3 units above the origin.
What is a graph?In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs (data points) on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.
Next, we would use an online graphing calculator to plot the above set of data points with a point of intersection at (2, 3) as shown in the graph attached below.
By critically observing graph B of the given set of data points, we can logically deduce that it correctly graphs the points A(3, 1), B(0, 3), and C (1, 3) as shown in the image attached below.
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Complete Question:
Which of the following grids correctly graphs the points A (3, 1), B (0, 3), and C (1, 3)?
A. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 3 units to the right and 1 unit above the origin. Point B is plotted 3 units to the right of the origin. Point C is plotted 1 unit to the right and 3 units above the origin.
B. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 3 units to the right and 1 unit above the origin. Point B is plotted 3 units above the origin. Point C is plotted 1 unit to the right and 3 units above the origin.
C. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 1 unit to the right and 3 units above the origin. Point B is plotted 3 units above the origin. Point C is plotted 3 units to the right and 1 unit above the origin.
D. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 1 unit to the right and 3 units above the origin. Point B is plotted 3 units to the right of the origin. Point C is plotted 3 units to the right and 1 unit above the origin.
What is the value of k in the function f(x)=2-k/5x-k if it passes through the point (3,-2/19)
The value of k from the equation is k = 4
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
f ( x ) = ( 2 - k ) / ( 5x + k ) be equation ( 1 )
Now , the equation passes through the point P ( 3 , -2/19 )
On simplifying the equation , we get
Substituting the values of x and y in the equation , we get
y = ( 2 - k ) / ( 5 ( 3 ) + k ) )
-2/19 = ( 2 - k ) / ( 15 + k )
Multiply by ( 15 + k ) on both sides of the equation , we get
-2 ( 15 + k ) / 19 = 2 - k
Multiply by 19 on both sides of the equation , we get
-30 - 2k = 38 - 19k
Adding 2k on both sides of the equation , we get
38 - 17k = -30
Subtracting 38 on both sides of the equation , we get
17k = 68
Divide by 17 on both sides of the equation , we get
k = 4
Hence , the value of k = 4
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The 11 students in the Environmental Club represent 5% of the students in the seventh grade. How many students are in the seventh grade?
Answer: 220
Step-by-step explanation:
Create ratios using fractions, one for the students, and one for the percent
students: [tex]\frac{11}{x}[/tex] percents: [tex]\frac{5}{100}[/tex]
Then cross multiply 1. [tex]11 *100 = 1100[/tex], 2. [tex]1100 / 5 = 220[/tex]
So [tex]x = 220[/tex], this means there are a total of 220 students in 7th grade
A company sells snow globes made out of glass that are in the shape of hollow
spheres. Nolan measures the outer diameter of a snow globe to be 30 cm. If
the glass has a thickness of 0.5 cm, find the total volume of glass that makes
up the globe. Round your answer to the nearest hundredth if necessary.
(Note: diagram is not drawn to scale.)
The total volume of glass that makes up the globe to the nearest hundredth is equal to 12,771.71 cubic centimeters.
How to calculate the volume of a sphere?Mathematically, the volume of a sphere can be calculated by using this mathematical expression:
Volume = 4/3 × πr³
Where:
r represents the radius.
Based on the information provided about the globe, the diameter of the hollow sphere is given by;
Diameter of sphere = 30 cm
Radius = diameter/2 = 30/2 = 15 cm.
Actual radius = 15 cm - 0.5 cm = 14.5 cm.
Substituting the given points into the volume of a sphere formula, we have the following;
Volume of sphere = 4/3 × 3.142 × 14.5³
Volume of sphere = 12,771.71 cubic centimeters.
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Consider two completely different data sets: price per gallon of gas in Fort Pierce and SAT scores of students
at a certain high school.
The price per gallon of gas data set has a mean of $2.05 and a standard deviation of $1.04.
The high school SAT scores data set has a mean of 1014 and a standard deviation of 160.
Calculate the Coefficient of Variation for both data sets. Round solutions to one decimal place, if necessary.
Coefficient of Variation for the price per gallon of gas data set:
Coefficient of Variation for high school SAT scores data set:
Which data set has greater variability? Price per gallon of gas
Thus, we see that when comparing two data sets, the data set with the larger standard deviation
necessarily have greater variabilty.
does not
CV stands for standard deviation divided by sample mean multiplied by 100.
How are CV and SD calculated?By applying the formula, she assesses: Example calculation: CV = standard deviation / sample mean x 100CV stands for standard deviation divided by sample mean multiplied by 100. CV also stands for volatility divided by expected return multiplied by 100.Price Variation (CV): The CV is the difference between the budgeted amount and the earned value of the task that was completed (Actual Cost). EV-AC = CV. - Schedule Variance (SV): The SV is the discrepancy between the earned value of work that has been completed and the planned value of work that has been scheduled. SV = EV – PV.CV = (std. deviation*100)/mean = 41.2 %
for SAT score:
CV = (std. deviation*100)/mean = 17.55%
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Please help. I'm really confused on how to solve this.
there is a line that includes the point(1,17) and has a slope of 1. What is its equation in slope-intercept form
An equation of the line in slope-intercept form that passes through the point (1, 17) and has a slope of 1 is equal to y = x + 16.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.Given the following parameters:
Point (x, y) = (1, 17)Slope = 1Substituting the given parameters into the point-slope formula, the equation of the line in is slope-intercept form given by;
y - y₁ = m(x - x₁)
y - 17 = 1(x - 1)
y = x - 1 + 17
y = x + 16
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now complete your visual overview by identifying the known variables and the variables you must find. assume charge 1 is located at the origin of the x axis and the positive x axis points to the right. let x1 , x2 , and x3 denote the positions of charge 1, charge 2, and charge 3, respectively. determine which of the following quantities are known and which are unknown.
The known quantities are then identified using the visual overview as a guide, and they are q1 q2 q3 x1 and x2. The unknown quantity is then x3
Based on the details provided;
e charge 1 is located at the origin of the x-axis and the positive x-axis points to the right. Let x1, x2, and x3 denote the positions of charge 1, charge 2, and charge 3, respectively
Considering that charge 1 is thought to be at the source;
The known quantities are then identified using the visual overview as a guide, and they are:
q1 q2 q3 x1 and x2
However, given that we are unsure of its precise position x3,
The unknown quantity is then x3
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Which graph matches the inequality y is greater than or equal to negative one third times x plus 1? The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line. The graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line. The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line. The graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line.
The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line.
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here: The inequality y≥ -x/3 +1
Now, To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.
Therefore y=-x/3 +1 is a line in slope-intercept form with slope=-1/3 and y-intercept 1
Thus the line should intersect the y-axis at y=1 and the x-axis at x=3
∴ The graph of this equation is plotted in attached file.
Hence, The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line.
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Answer:
A
Step-by-step explanation:
i took the test xx
Solve the following question:
|p+2|=5
Which of the following points satisfies y < 3x - 6?
(2, -4)
(1,0)
The point (2,-4) satisfies y < 3x - 6
The sum of two numbers is 8 more than four times the first number. Their difference is 10 less than three times the second number. Find each of the numbers.
Answer:
first number= -2 and the second number = 2
Step-by-step explanation:
x= one number and y= the other
your two equations are x+y=4x+8 and x-y=3y-10
by solving the first one for y, y=3x+8 so plug that in for y in the second equation
x-(3x+8)=3(3x+8)-10
x-3x-8=9x+24-10
-2x-8=9x=14
11x=-22 so x=-2
now plug that in and solve for y
-2+y=4(-2)+8
y=2
please help will mark BRAINLIEST
Help help help help help help help
Answer: with ?
Step-by-step explanation:
Math help linear function
Answer:
Choice B
Step-by-step explanation:
The y increases by 3 every time that the x increases by 1.
Hope this helped! :)
A contractor bought 8.2^2 ft of sheet metal. has used 3.7^2 ft so far and has $90 worth of sheet metal remaining. The equation 8.2x - 3.7x = 90 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
Answer:
$20 per square foot
Step-by-step explanation:
[tex]8.2x-3.7x=90 \\ \\ 4.5x=90 \\ \\ x=20[/tex]
Unsure how to do my Algebra homework!
On solving the exponential function 16000 = P(0.9455)^t, the original value of the car is obtained as $18,930.
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The value of car in amount is A(t) = $16,000.
The rate of depreciation is x = 5.45% per year.
Rewriting the rate in exponential form - (1 - 0.0545) = 0.9455
The car is t = 3 years old.
Let P be the model that depicts the original cost of the car.
Then the exponential function will be -
16000 = P(0.9455)^t
Substituting the value of t in the equation -
16000 = P(0.9455)³
16000 = 0.8452P
P = 16000/0.8452486
P = 18,929.34 ≈ 18,930
Therefore, the original value of car was $18,930.
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the mid point of AB is M(-4,-3). If the coordinates of A are (-1,-2), what are the coordinates of B?
If the mid point of AB is M (-4,-3). and the coordinates of A are (-1,-2), the coordinates of B is solved to be (-7, -4)
What is midpoint of a line?The midpoint of a line segment is the centroid of the segment. It is equally distant from both of the ends and hence cuts the section in half.
How to find the second point of the line segmentThe formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.
The formula is of the form
X= (x₂ + x₁)/2
Y = (y₂ + y₁)/2
From the formula the second end point is calculated
-4= (-1 + x₁)/2
-8 = -1 + x₁
x₁ = -7
-3 = (-2 + y₁)/2
-6 = -2 + y₁
y₁ = -4
The coordinates of B are (-7, -4)
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0.056 divided by 4,939.0977
A point P is on the terminal side of angle θ. Evaluate six trigonometric functions for θ.
P(2, -7)
The exact values of the trigonometric functions for an angle are:
Sine: - 7√53 / 53 Cosine: 2√53 / 53 Tangent: - 7 / 2 Cotangent: - 2 / 7 Secant: √53 / 2 Cosecant: - √53 / 7How to derive the six trigonometric functions of the terminal side of an angle
The direction of an angle (θ), in degrees, with respect to origin is determine by coordinates on the terminal side. For a point in rectangular format we can determine the exact values of two fundamental trigonometric functions (sine, cosine) and four derivate trigonometric functions (tangent, cotangent, secant, cosecant:
For P(x, y) = (x, y)
Sine
sin θ = y / √(x² + y²)
Cosine
cos θ = x / √(x² + y²)
Tangent
tan θ = sin θ / cos θ
Cotangent
cot θ = 1 / tan θ
Secant
sec θ = 1 / cos θ
Cosecant
csc θ = 1 / sin θ
If we know that x = 2 and y = - 7, then exact values of trigonometric functions are, respectively:
Sine
sin θ = - 7 / √[2² + (- 7)²]
sin θ = - 7 / √53
sin θ = - 7√53 / 53
Cosine
cos θ = 2 / [2² + (- 7)²]
cos θ = 2 / √53
cos θ = 2√53 / 53
Tangent
tan θ = [- 7√53 / 53] / [2√53 / 53]
tan θ = - 7 / 2
Cotangent
cot θ = 1 / (- 7 / 2)
cot θ = - 2 / 7
Secant
sec θ = 1 / (2 / √53)
sec θ = √53 / 2
Cosecant
csc θ = 1 / (- 7 / √53)
csc θ = - √53 / 7
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A baker makes 60 muffins. He sells 24 of the muffins.
He put the rest of the muffins in boxes. Each box can hold 4 muffins.
Which equation can be used to find b, the number of boxes the baker will need?
OA.
B.
OC.
OD. (60
60+ 24 ÷ 4 = b
60 24 ÷ 4 = b
-
(60+24) ÷ 4 = b
24) = 4 = b
-
Answer:c
Step-by-step explanation:
c
Answer:b
Step-by-step explanation:
Suppose f(x) = x2. What is the graph of g(x) = f(2x)?
The required function g(x) = 4x² and the related graph is a parabola that is opened upwards on the x-axis
Graph of a function?The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. This means that when we replace x - coordinate with a numerical value in the expression, we get the y-value for the given function f(x).
Here we have
f(x) = x²
Given that g(x) = f(2x)
To find the g(x) take x = 2x
=> f(2x) = (2x)²
=> g(x) = 4x²
Therefore,
The required function g(x) = 4x² and the related graph is a parabola that is opened upwards on the x-axis
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
The statements which are always true in the triangle with interior angles, ∠2, ∠3, and m∠5, and exterior angles, ∠1, ∠4, and ∠5 are;
m∠5 + m∠6 = 180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 180°
What is an exterior angle of a triangle?An exterior angle is an angle that is formed by the extension of a side of the triangle and the side adjacent to the extended side.
The interior angles of the triangle are; angle ∠2, angle ∠3, and angle ∠5
The exterior angles at the interior angles of the triangle ∠2, ∠3, and ∠5 are angles ∠1, angle ∠4, and angle ∠6 respectively.
Therefore, according to the exterior angle theorem, we get;
m∠1 = m∠3 + m∠5
m∠4 = m∠2 + m∠5
m∠6 = m∠2 + m∠3
The exterior angle and the adjacent internal angle are supplementary angles, therefore;
m∠2 + m∠1 = 180°
m∠3 + m∠4 = 180°
m∠5 + m∠6 = 180°
The angle sum property of a triangle indicates that the sum of the interior angles of a triangle is 180°, therefore;
m∠2 + m∠3 + m∠5 = 180°
The statements that are always true are therefore;
m∠5 + m∠6 = 180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
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Let f(x) = 2x+4 and g(x)=4x^2+4х.
After simplifying,
(f o g) (x)=
If looking at what I wrote is confusing I added a photo to help
The simplified form of (f o g)(x) = 8x² + 8x + 4.
What is differentiation?Differentiation is a process in calculus that is used to find the rate of change of a function at a specific point. It is the process of finding the derivative of a function.
To find (f o g)(x), we need to first find g(x) and then substitute that expression into f(x).
Given:
f(x) = 2x + 4
g(x) = 4x² + 4x
So:
(f o g)(x) = f(g(x)) = f(4x² + 4x) = 2(4x² + 4x) + 4
Now we can substitute the expression for g(x) into f(x) and simplify:
= 2(4x² + 4x) + 4 = 8x² + 8x + 4
Hence, (f o g)(x) = 8x² + 8x + 4
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Select the statement that is false.
Select one:
a. If 4 is a prime number, then 6 is a prime number.
b. If 4 is a prime number, then 5 is a prime number.
c. If 3 is a prime number, then 5 is a prime number.
d. If 3 is a prime number, then 6 is a prime number
Out of the given statements, statement a. If 4 is a prime number, then 6 is a prime number is the false one. A prime number is a positive integer that has exactly two distinct natural number divisors: 1 and itself.
For example, the number 2 is a prime number because it can only be divided evenly by 1 and 2. 4 is not a prime number because it can be divided evenly by 1, 2, and 4. 6 can be divided evenly by 1, 2, 3, and 6, so it is not a prime number. Therefore, statement a is false because if 4 is a prime number, 6 is not a prime number.
When determining whether a number is a prime number, it is important to remember that 1 is not a prime number. This is because 1 only has one divisor - itself. Any other number that can be divided evenly by more than two distinct natural numbers is not a prime number.
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Which of the following is an equivalent expression to 7.5+s using commutative property?
An equivalent expression to 7.5 + s using commutative property is; s + 7.5
How to use the commutative property of algebra?
The commutative property under addition is an algebra property that states that the change in the order of numbers in an addition operation does not change the sum.
This means that for any real numbers x, y, we have;
x + y = y + x
The commutative property under multiplication states that the change in the order of numbers in multiplication operation does not change the product.
This means that for any real numbers c, d we have;
c × d = d × c
We want to find n equivalent expression to 7.5 + s using commutative property. Thus, we will apply the commutative property of addition as followd; 7.5 + s = s + 7.5
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Select the correct answer. What is the equation of a line passing through (-6, 5) and having a slope of 1 3 ? A. y = 1 3 x − 23 3 B. y = 1 3 x − 3 C. y = 1 3 x + 7 D. y = 3x + 7 Reset Next
Answer:
C
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = [tex]\frac{1}{3}[/tex] , then
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (- 6, 5 ) into the partial equation
5 = [tex]\frac{1}{3}[/tex] (- 6) + c = - 2 + c ( add 2 to both sides )
7 = c
y = [tex]\frac{1}{3}[/tex] x + 7 ← equation of line