Question

Write the point-slope form of the line that passes through (-8, 2) and is parallel to a line with a slope of -8. Include all of your work in your final answer. Type your answer in the box provided to submit your solution.

Answer 1

y - 2 = -8(x + 8)

Explanation:

Parallel lines have equal slope

Therefore, the slope of the line that passes through (-8, 2) is equal to -8 which is also the slope of the line parallel to it.

The slope of a line is given by

m = (y - y1) / (x - x1)

m = -8

Point (-8, 2) corresponds to (x1, y1)

Therefore, x1 = -8; y1 = 2

In, m = (y - y1) / (x - x1), we substitute the known values

-8 = (y - 2) / (x - (-8))

-8 = (y - 2) / (x + 8)

Cross multiply

y - 2 = -8(x + 8)

The point-slope form of the equation of a line is written as

y - y1 = m(x - x1)

In comparison,

y - y1 = m(x - x1) is equivalent to

y - 2 = -8(x + 8)

Therefore, the point-slope form of the line that passes through (-8, 2) and is parallel to a line with a slope of -8 is

y - 2 = -8(x + 8)