Question

the points (2, -1) and (r, 9) lie on a line with slope 2. find the missing coordinate r.

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 $(x_1,y_1)=(2,-1)$, $(x_2,y_2)=(r,9)$, and $m=2$. Substitute into the formula:
$2=\frac{9-(-1)}{r-2}$

Step3: Simplify numerator

Calculate $9-(-1)=10$, so:
$2=\frac{10}{r-2}$

Step4: Solve for $r-2$

Multiply both sides by $r-2$, then divide by 2:
$r-2=\frac{10}{2}=5$

Step5: Solve for $r$

Add 2 to both sides:
$r=5+2$

Answer:

$7$