Question

1. what is the equation of a line parallel to y = 7x - 8 that passes through (5, -2)?

Explanation:

Step1: Identify the slope

Parallel lines have the same slope. The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope. For the line $y = 7x-8$, the slope $m = 7$.

Step2: Use the 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. We have $m = 7$ and the point $(x_1,y_1)=(5, - 2)$.
Substitute these values into the point - slope form: $y-(-2)=7(x - 5)$.

Step3: Simplify the equation

$y + 2=7x-35$.
Subtract 2 from both sides to get the slope - intercept form: $y=7x-37$.

Answer:

$y = 7x-37$