Write an equation, in slope-intercept form, for the line that passes through the point (-8, 7) and is parallel to the line y=− 2/3x−6

Answer 1

Since we need an equation in slope-intercept form, let's focus on finding just those two pieces:

1. Slope: since we want this line to be parallel to y=-2/3x - 6, we want our new line to never intersect this first line. We can do that by choosing a line with the same exact slope, m=-2/3, which ensures that both of our lines will increase at the same exact rate.
2. Y-intercept: right now, our new line looks like y=-2/3x + b, and now we need to figure out b. Thankfully, we're given a point that this line must pass through, so we can just plug that in:

y=-2/3x + b

7=-2/3*(-8) + b

7=16/3 + b

b = 5/3

With our slope and y-intercept, we're done! Our line is:

y = -2/3x + 5/3

Answer 2

Parallel lines have the same slope, so the slope of the line parallel to the line with equation y = -(2/3)x - 6 is -2/3.

Equation of line is y = -(2/3)x + b.

Plug in the point (-8, 7) and solve for b.