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 slope - intercept form $y=mx + b$ and substitute one of the points and the slope. Let's use the point $(7,1)$ and $m = 1$. So $1=1\times7 + b$. Solving for $b$ gives $b=1 - 7=-6$.

Step3: Write the equation

The slope - intercept form of the line is $y=mx + b$. Substituting $m = 1$ and $b=-6$, we get $y=x - 6$.

Answer:

$y=x - 6$