Correction of a math problem

Question

Write an equation of the line that asses through(3,-2) and is parallel to the line y=9x-6

Answer 1

The given line has its equation written in slope-intercept form so it is easy to identify its slope (m = 9).

Parallel lines have the same slope, so we are looking for the line passing through (3,-2) with a slope of 9.

There are basically two ways to take if from here.

I. Substitute into the point-slope form (my preference) and return to slope-intercept form (if required):

y - (-2) = 9 (x - 3)

y+2 = 9x - 27

y = 9x -29

II. Substitute into slope-intercept form then solve for "b".

-2 = 9(3) + b

-2 = 27 + b

b = -29.

y = 9x -29

The two lines have the same slope, but different y-intercepts, so they are parallel.

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