Question

1. line a is represented by the equation 8x + 2y = 16. line b is parallel to line a and passes through the point (- 9, - 9). write the equation of line b in slope - intercept form.

Explanation:

Step1: Rewrite Line A in slope - intercept form

First, solve the equation of Line A $8x + 2y=16$ for $y$.
Subtract $8x$ from both sides: $2y=-8x + 16$.
Divide by 2: $y=-4x + 8$. The slope of Line A is $m=-4$. Since Line B is parallel to Line A, the slope of Line B is also $m=-4$.

Step2: Use the point - slope form to find the equation of Line B

The point - slope form is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-9,-9)$ and $m = - 4$.
Substitute the values: $y-(-9)=-4(x - (-9))$.
Simplify: $y + 9=-4(x + 9)$.

Step3: Convert to slope - intercept form

Expand the right side: $y+9=-4x-36$.
Subtract 9 from both sides: $y=-4x-45$.

Answer:

$y=-4x - 45$