Is the line through points p (3,-5) and Q(1,4)parallel to the line through points R( -1,1) and S (3,-3)

Answer:

No

Step-by-step explanation:

To find out if the lines that go through the pairs of points are parallel, we must find the slope of each line. If the slopes are equivalent, then they are parallel. If not, then they are not parallel.

We can use the slope formula to find the slope between two points. The slope formula is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

where m is the slope between the points (x₁, y₁) and (x₂, y₂).

Lets first find the slope between points P and Q.

[tex]m=\frac{-5-4}{3-1}=\frac{-9}{2}=-4.5[/tex]

So the slope between P and Q is -4.5.

Now lets find the slope between the points R and S.

[tex]m=\frac{-3-1}{3-(-1)}=\frac{-4}{4}=-1[/tex]

So the slope between R and S is -1.

Since -4.5 does not equal -1, the lines are not parallel.

I hope you find my answer and explanation to be helpful. Happy studying.

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