Mathematics High School

18. Write the equation of the following line in function notation

18. Write The Equation Of The Following Line In Function Notation

Answers

Answer 1

Answer:

[tex]\LARGE\mathsf{f(x)\:=-\frac{3}{4}x\:+\:-\frac{5}{4}}[/tex]

Step-by-step explanation:

Slope:

Given the two points from the graph, (-3, 1) and (1, -2). Use these points to solve for the slope using the following formula:

[tex]\LARGE\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}[/tex]

Let (x₁, y₁) = (-3, 1)

     (x₂, y₂) = (1, -2)

Substitute these points into the formula:

[tex]\LARGE\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}[/tex]

[tex]\LARGE\mathsf{m = \frac {-2\: -\: 1}{1\: -\: (-3)}\:=\:\frac {-2\: -\: 1}{1\: +\:3}\:=\frac{-3}{4}}[/tex]

m = -¾

Therefore, the slope of the given line is -¾.

Y-intercept:

Next, we need to determine the y-intercept, which is the point on the graph where it crosses the y-axis.  In order to solve for the y-intercept, we must use the slope, m = -¾, and one of the given points, (1, -2), and substitute these values into the slope-intercept form,  f(x) = mx + b:

f(x) = mx + b

-2 = -¾( 1 ) + b

-2 = -¾ + b

Add ¾ to both sides to solve for b:

-2 + ¾ = -¾ + ¾ + b

[tex]\LARGE\mathsf{y-intercept\:(b)\:=\:-\frac{5}{4} }[/tex]

Equation of the Line in Function Notation:

Given the slope, m = -¾, and y-intercept, b = [tex]\LARGE\mathsf{-\frac{5}{4}}[/tex], the equation of the line in function notation is:

[tex]\LARGE\mathsf{f(x)\:=-\frac{3}{4}x\:+\:-\frac{5}{4}}[/tex]

Related Questions

Hello please help with this question.

Answers

Answer:

77.32°

Step-by-step explanation:

Use sine to find the measure of ∠A:

sine = opposite / hypotenusesin A = 80/82m∠A = arcsin (80/82) = 77.32°

i just want to make question of this simplify plz solve question fast​

Answers

Answer:

I believe 100

Step-by-step explanation:

He had 18 then got 32 from his mom leaving him with 50 and tripled it so 150 and he gave 25 to both his sister so 25+25=50 so 150-50=100

please give brainliest

I GIVE BRANLIEST. Question is on the bottom

Answers

Answer:

432

24*36

---------- = 432

2

A rectangle measures 2 2/5 inches by 4 1/8 inches. What is its area

Answers

Answer:

A = 9 9/10 sq inches

Step-by-step explanation:

A = lw

A = 12/5 x 33/8

A = 396/40

A = 9 9/10 sq inches

The cost of Matt and Natalie's dinner was $27.35. They want to leave a 20% tip. Which of the following is the closest to the amount of the tip they want to leave?
A. $4.00
B. $4.50
C. $5.00
D. $5.50

Answers

Answer:

Option D is correct.

Step-by-step explanation:

27.35 x 20/100

=> 2.735 x 2/1

=> $5.47

=> $5.50 (Rounded)

Therefore, Option D is correct.

Hoped this helped.

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Answers

All are relations except for relation 3

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Answers

2y - 3 = 4y + 6

Subtract 6 from both sides

2y -9 = 4y

Subtract 2y from both sides

-9 = 2y

Divide both sides by 2

Y = -9/2 or -4.5 as a decimal

Increase 80 by 12.5%

Answers

Answer:

90

Step-by-step explanation:

Answer:

[tex]80 \times \frac{12.5}{100} \\ = 10 [/tex]

then 80+10 =90

Pls help, I need (c) of the problem 3-106

Answers

Answer:

Negative x minus two

Step-by-step explanation:

3 - (x + 5)

Distribute the negative sign:

3 - x - 5

Simplify:

-x - 2

In words:

Negative x minus two

Solve the given equation

x – 1 + 5x = 23

Answers

Step-by-step explanation:

x - 1 + 5x = 23

6x - 1 = 23

6x = 23 + 1 = 24

6x = 24

x = 24/6

x = 4 ans.

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE.

Suppose y varies jointly as x and z. What is y when x = 2 and z = 3, if y = 20 when x = 4 and z = 3?

Answers

Answer:

y = 10

Step-by-step explanation:

Given y varies jointly as x and z then the equation relating them is

y = kxz ← k is the constant of variation

To find k use the condition y = 20 when x = 4 and z = 3 , then

20 = k × 4 × 3 = 12k ( divide both sides by 12 )

[tex]\frac{20}{12}[/tex] = k , that is

k = [tex]\frac{5}{3}[/tex]

y = [tex]\frac{5}{3}[/tex] xz ← equation of variation

When x = 2 and z = 3 , then

y = [tex]\frac{5}{3}[/tex] × 2 × 3 = 5 ×  2 = 10

help please
denominator only

Answers

Answer:

2+3=5 3-5=2

Step-by-step explanation:

that's the answer

Percy has a coin collection. He has five pennies for every 33 dimes. If Percy has 1515 pennies what is the total number of coins in his collection?

Answers

Answer:

1515

Step-by-step explanation:

PLS HELP WILL MARK BRAINLIEST, PLS HURRY

Answers

multinomial, i believe
hope this helps!

PLEASE HELP The mean life expectancy of a certain type of light bulb is 860 hours with a standard deviation of 22 hours.

What is the approximate standard deviation of the sampling distribution of the mean for all samples with n = 65?


0.34 h


0.75 h


2.73 h


2.95 h

Answers

0.34 h is my take on the answers

Answer: The correct answer is: 2.73 h.

Step-by-step explanation:

I hope this helps! :)

40% of students surveyed said
that they are night owls. If 300
students said they are night
owls, how many students were
surveyed?

Answers

Answer:

750 students.

Step-by-step explanation:

Someone pls pls pls help ASAP
I’ll give brainliest I promise just pls help me

Answers

Answer:

Answer attached below.

I really need help with this one it's due today!!

Answers

Answer:

-2/3

3/2

Step-by-step explanation:

So to have a line parallel the equation is: m1 = m2, meaning the slope (represented by m in this equation) is equal. So in the equation. 3y = - 2x + 4 you need to simplify the equation by dividing both sides by 3. Which would be like so: y = - 2/3x + 4/3, which the slope will be -2/3.

To be perpindicular you need the slope to be: m1 * m2 = - 1. So because we already know that the slope is -2/3, all we need to do is set up an equation: -2/3 * y = - 1

-2/3y = - 1

multiply both sides by 3/-2

y = 3/2

What is the slope of this line?

Enter your answer as a whole number or a fraction in simplest form in the box.

Answers

Answer:

1/4

Step-by-step explanation:

use 2 points from the graph (-4,5) and (0,6) and  put them in the distance equation.

(y2-y1)

----------

(x2-x1)

6-5

-------

0-(-4)

1/4

What is the measure of ZPRQ?
P
O
A. 172°
1020
B. 70°
70"
s
C. 86°
D. 1020

Answers

Answer: should be 86°, not sure.

Step-by-step explanation:

: Mr. Burkett drove his car at an average speed of 70 miles per hour for 3.5 hours and then traveled at an

average speed of 65 miles per hour for 2.5 hours. What was the total distance in miles that he traveled during this time?

Answers

Answer:

Mr Burkett travelled 407.5 miles during his full trip.

Step-by-step explanation:

First, we must determine the distance he travelled in the first 3.5 hours. Luckily, we know his speed during that time so we can just multiply 70 miles per hour by 3.5 hours. That is 245 miles.

In the second step, we must determine the distance he travelled during the second part of his trip where he slowed down a bit. 65 miles per hour times 2.5 hours is 162.5 miles.

Finally, we can just add them! 245 + 162.5 = 407.5.

help me with math!!!!

Answers

Answer:

5+4 < 10+2

Step-by-step explanation:

5+4=9

10+2=12

simplify √5(8+3√6)
I cant figure this problem out can someone help me?

Answers

The answer is correct

dont mind this i just need the achivement

Answers

Answer:

K cool

Step-by-step explanation:

Answer:

Step-by-step explanation:

Please show your graph if you’re in K12, no confusing graphs please. graph the line for y + 1= - 3/5 (x-4)

Answers

Answer:

Graph Below:

How to find area of a triangle.

Answers

Base x height divided by 2

Carlisle purchased one-fourth of a pound of candy at the mall. What decimal did he see on the scale?


0.25

0.40

0.20

0.14

Answers

the answer is 0.25 1 divided by 4 is 0.25
The answer is .25, when you divide 1 by four you get .25

HELPPP PLEASEEEE………..

Answers

Answer:

the answer is 54°......

How to find the distance between two points.

Answers

Answer:

you take your small number and multiply it by the big number

Step-by-step explanation:

Find the values of x and y.

Answers

70+35=105
180-105=75(sum of angle in a triangle is 180)
180-75=105(cyclic angles are equal to 180)
105+70=175
180-175=5 (sum of angle in a triangle is 180)
5x=5
X=1
Y=105
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