Line 1 passes through the point (-4,-7)and (2,3) on the coordinates plane.line 2 passes through the point (-4,1) and (2,w).for what value of w is line 2 parallel to line 1

Question

Choice:

11

-3

4

1

Answer 1

The slopes of parallel lines are equal so we need to figure out the slope of line 1 first.

It will be (3 - (-7))/(2 - (-4))= 10/6 = 5/3.

For the second line we get (w -1 )/(2 - (-4)) = (w - 1)/6

We set that equal to 5/3.

(w - 1)/6 = 5/3..

Multiply both sides by 6 we get

w - 1 = 10

Add 1 to both sides we get w = 11.

Since we got 6 in the denominator of both slopes, we could have just set w - 1= 10 and got w = 11 again. However, this is not the case with most of these problems.

Answer 2

For the lines to be parallel they need to have the same slope. Given 2 points, let's use the slope equation.

m= (y₂-y₁)/(x₂-x₁)

Line 1: m= (3-(-7))/(2-(-4)) = 10/6

Line 2: m= (w-1)/(2-(-4)) = (w-1)/6

Therefore w must be 11 in order to get the same slope as line 1 which is 10/6