Question

find the value of k so that the lines that pass through the following points are parallel: line 1: (0,3) and (-2,4) and line 2: (k,-1) and (5,7)

Answer 1

For lines to be parallel, the slopes have to be the SAME.

To find the value of k, you can first find the slope of line 1 using the slope(m) formula, and plug in the points:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m = \frac{4-3}{-2-0}$

$m = \frac{1}{-2}$

Now that you know the slope, you can use the slope formula to find k by plugging in what you know:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$-\frac{1}{2} = \frac{7-(-1)}{5-k}$  Multiply (5 - k) on both sides

$-\frac{1}{2} (5 - k) = 7 - (-1)$  Multiply -2 on both sides

5 - k = -2(7 + 1)

5 - k = -2(8)

5 - k = -16 Subtract 5 on both sides

-k = -21 Divide -1 on both sides

k = 21

Answer 2

1) as the lines  are parallel  then have the same slope , it  means that we can obtain the slope with the points of the line 1 with the following formula

m= y2-y1/ x2-x1 ⇒m = 4-3/-2-0 = -1/-2 = 1/2,

2) now to obtain k

1/2 = 7-(-1)/5-k⇒ 1/2 (5-k) = 7+1⇒5-k = 2(7+1) ⇒5-k= 14+2⇒-k = 16-5⇒-k = 12⇒k=-12