Question

1. a line has a slope of $\frac{9}{7}$ and includes the points (2, 10) and (z, 1). what is the value of z?

$z = \square$

Explanation:

Step1: Recall slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.

Step2: Substitute known values

Let $(x_1,y_1)=(2,10)$, $(x_2,y_2)=(z,1)$, and $m=\frac{9}{7}$.
$\frac{9}{7}=\frac{1-10}{z-2}$

Step3: Simplify numerator

Calculate $1-10=-9$.
$\frac{9}{7}=\frac{-9}{z-2}$

Step4: Cross-multiply to solve for z

$9(z-2)=7\times(-9)$
$9z-18=-63$

Step5: Isolate z term

Add 18 to both sides.
$9z=-63+18=-45$

Step6: Solve for z

Divide both sides by 9.
$z=\frac{-45}{9}=-5$

Answer:

$z=-5$