Question

a line passes through point (-2, -8) and has a slope of 7.
write an equation in ax + by = c form for this line.
use integers for a, b, and c.

Explanation:

Step1: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope. Here, $x_1=-2$, $y_1 = - 8$ and $m = 7$. So we substitute these values into the point - slope form: $y-(-8)=7(x - (-2))$, which simplifies to $y + 8=7(x + 2)$.

Step2: Expand the right - hand side

Expand $7(x + 2)$ using the distributive property $a(b + c)=ab+ac$. So $y + 8=7x+14$.

Step3: Rearrange to $Ax+By = C$ form

Subtract $y$ from both sides and subtract 14 from both sides to get $7x-y=-6$.

Answer:

$7x - y=-6$