Question

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

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-1,-7)$ and $(x_2,y_2)=(7,1)$. Then $m=\frac{1-(-7)}{7-(-1)}=\frac{1 + 7}{7+1}=\frac{8}{8}=1$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(7,1)$ and $m = 1$. So $y - 1=1\times(x - 7)$. Expand it: $y-1=x - 7$. Add 1 to both sides to get the slope - intercept form $y=x-6$.

Answer:

$y=x - 6$