Question

the points (g, 5) and (-1, -2) fall on a line with a slope of $-\frac{7}{2}$. what is the value of g?
$g = \square$
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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, $m=-\frac{7}{2}$, $(x_1,y_1)=(g,5)$, $(x_2,y_2)=(-1,-2)$.
Substitute into formula: $-\frac{7}{2}=\frac{-2-5}{-1-g}$

Step2: Simplify numerator

Calculate $-2-5=-7$, so:
$-\frac{7}{2}=\frac{-7}{-1-g}$

Step3: Solve for $g$

Cross-multiply: $-7(-1-g)=-7\times2$
Simplify left side: $7+7g=-14$
Subtract 7 from both sides: $7g=-14-7=-21$
Divide by 7: $g=\frac{-21}{7}=-3$

Answer:

$g=-3$