Question

a line with a slope of \\(\frac{8}{3}\\) passes through the points \\((6, g)\\) and \\((9, 1)\\). what is the value of \\(g\\)?
\\(g = \square\\)

Explanation:

Step1: Recall slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.
Here, $m=\frac{8}{3}$, $(x_1,y_1)=(6,g)$, $(x_2,y_2)=(9,1)$. Substitute into formula:
$\frac{8}{3}=\frac{1-g}{9-6}$

Step2: Simplify denominator

Calculate $9-6=3$, so:
$\frac{8}{3}=\frac{1-g}{3}$

Step3: Eliminate denominators

Multiply both sides by 3:
$8=1-g$

Step4: Solve for $g$

Rearrange to isolate $g$:
$g=1-8$

Answer:

$g=-7$