a line passes through the points (-1, -8) and (1, 6). write its equation in slope - intercept form. write…

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-1,-8)$ and $(x_2,y_2)=(1,6)$. Then $m=\frac{6-(-8)}{1 - (-1)}=\frac{6 + 8}{1+1}=\frac{14}{2}=7$.

Step2: Find the y - intercept

Use the slope - intercept form $y=mx + b$ and one of the points, say $(1,6)$. Substitute $x = 1$, $y = 6$ and $m = 7$ into $y=mx + b$. We get $6=7\times1 + b$. Solving for $b$: $b=6 - 7=-1$.

Step3: Write the equation

The equation of the line in slope - intercept form is $y=mx + b$. Substituting $m = 7$ and $b=-1$, we have $y = 7x-1$.

Answer:

$y = 7x-1$