Question

1. write the equation in slope-intercept form of the line that passes through (-1,11) and is parallel to the graph of y = -8x - 2.

Explanation:

Step1: Determine the slope

Parallel lines have the same slope. The given line \( y = -8x - 2 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope. So the slope of the given line is \( m=-8 \), and the slope of the line we want to find is also \( m = - 8 \).

Step2: 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. We know that \( m=-8 \) and the point \( (-1,11) \) (so \( x_1=-1 \), \( y_1 = 11 \)) is on the line. Substitute these values into the point - slope form:
\( y-11=-8(x - (-1)) \)
Simplify the right - hand side: \( y - 11=-8(x + 1) \)

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y-11=-8x-8 \)
Add 11 to both sides of the equation to solve for \( y \):
\( y=-8x-8 + 11 \)
Simplify the constants: \( y=-8x + 3 \)

Answer:

\( y=-8x + 3 \)