Question

A line through the points $(2, -9)$ and $(j, 17)$ is parallel to the line $2x + 3y = 21$. What is the value of $j$?

Answer 1

Answer:

j=-37

Step-by-step explanation:

step 1

Find the slope of the given line

we have

$2x+3y=21$

Convert to slope intercept form

Isolate the variable y

subtract 2x both sides

$3y=-2x+21$

divide by 3 both sides

$y=-\frac{2}{3}x+7$

The slope is

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

step 2

we have the points

(2,-9) and (j,17)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{17+9}{j-2}$

$m=\frac{26}{j-2}$

Remember that

If two lines are parallel then their slope are equal

therefore

$\frac{26}{j-2}=-\frac{2}{3}$

$26(3)=-2(j-2)\\78=-2j+4\\2j=4-78\\2j=-74\\j=-37$