Question

a line that includes the points (0, -10) and (9, d) has a slope of \\(\frac{8}{9}\\). what is the value of d?\\(d = \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 given values

Let $(x_1,y_1)=(0,-10)$, $(x_2,y_2)=(9,d)$, and $m=\frac{8}{9}$. Substitute into the formula:
$\frac{8}{9}=\frac{d-(-10)}{9-0}$

Step3: Simplify denominator

Simplify the right-hand side denominator:
$\frac{8}{9}=\frac{d+10}{9}$

Step4: Solve for $d$

Multiply both sides by 9:
$8 = d + 10$
Subtract 10 from both sides:
$d=8-10$

Answer:

$d=-2$