Question

Find the equation of the line that is parallel to y=-2/3x and contains the point (4,-8)

Answer 1

y = (-2/3)x + 16/3

Explanation:

Any line parallel to y = (-2/3)x has the same slope: (-2/3).

Then, in this pattern, y = (-2/3)x + c, where c is the y-intercept.

If (4, -8) lives on this new line, then:

-8 = (-2/3)(4) + c, and

-8 = -8/3 + c

This last equation is equivalent to -24/3 + 8/3 + c => -16/3 = -c.

Therefore the y-intercept is 16/3 = c, and the desired equation is

y = (-2/3)x + 16/3