Find an equation

Question

for the line perpendicular to the line 9x-y=3 having the same y-intercept as -5x+7y=6

Answer 1

Since the equations for both lines are given in Standard Format, we may assume that the answer should be in Standard Format also.

If you convert the Standard Format of a line (Ax+By=C) to slope-intercept format (y=mx+b) [PLZ do this once and forever], you will find:

slope m = -A/B

y-intercept = C/B (the value of y when x=0)

The perpendicular line has slope that is negative reciprocal of m. That is, B/A

The equation of the perpendicular line (in Standard Form) is:

x + 9y = 6/7

or, with all coefficients as integers,

7x + 63y = 6

Answer 2

9x - y = 3 rearrange to slope intercept to easily identify the slope of the line. y = 9x -3 therefore the slope is 9. The line perpendicular to this line has to have the inverse reciprocal (flip the fraction and take the opposite) therefore the perpendicular line has a slop of -1/9.

-5x + 7y = 6 needs to be rearranged into the same form to identify the intercept. y = 5/7x + 6/7. Intercept is 6/7.

Therefore the answer to the question is y = -1/9 + 6/7