Question

the points (9, g) and (10, -1) fall on a line with a slope of -2. what is the value of g?

Explanation:

Step1: Recall slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(9,g)$ and $(x_2,y_2)=(10, - 1)$, and $m=-2$.

Step2: Substitute values into slope - formula

Substitute the values into the formula: $-2=\frac{-1 - g}{10 - 9}$.

Step3: Simplify the right - hand side

Since $10 - 9 = 1$, the equation becomes $-2=-1 - g$.

Step4: Solve for g

Add 1 to both sides of the equation: $g=-1 + 2$.

Answer:

$g = 1$