Question

a line passes through the points (7, 1) and (-4, -8). write its equation in slope - intercept form.
use your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)=(7,1)$ and $(x_2,y_2)=(-4,-8)$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{-8 - 1}{-4 - 7}=\frac{-9}{-11}=\frac{9}{11}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(7,1)$ and $m = \frac{9}{11}$, we have $y - 1=\frac{9}{11}(x - 7)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y-1=\frac{9}{11}x-\frac{63}{11}$. Then add 1 to both sides. Since $1=\frac{11}{11}$, we get $y=\frac{9}{11}x-\frac{63}{11}+\frac{11}{11}=\frac{9}{11}x-\frac{52}{11}$.

Answer:

$y=\frac{9}{11}x-\frac{52}{11}$