Find an equation for the line perpendicular to the line −6x−2y=8 having the same y-intercept as 7x+6y=−7.

Answer 1

Start by calculating the slope of -6x - 2y = 8. To do that, manipulate the equation into the slope-intercept format y = mx + b and then whatever is in front of the "x" will be the slope.

-6x - 2y = 8

-6x = 8 + 2y

-6x - 8 = 2y

-3x - 4 = y

y = -3x - 4

So the slope is "-3"

To get the slope of the line perpendicular, take the negative reciprocal. Get the reciprocal by just flipping it over. To do so, think of -3 as -3/1. The reciprocal is -1/3. The negative of that is 1/3. So the slope of the line perpendicular to -6x - 2y = 8 is 1/3.

Now find the y-intercept of 7x + 6y = -7 by also manipulating it into y = mx + b. The number at the end (b) will be the y-intercept.

7x + 6y = -7

6y = -7x - 7

y = (-7/6)x - 7/6

So the y-intercept is -7/6, meaning the line goes through (0, -7/6)

Now, we have the slope of our line (m = 1/3) and the y-intercept of our line (b = -7/6) so we use y = mx + b and plug them in:

y = (1/3)x - 7/6