Question

Equation for the line perpendicular to the line -6x-7y=-6 having the same y-intercept as 8x-5y=10

Answer 1

Solving   8x-5y=10   for y helps us to identify the y-intercept:

-5y = -8x + 10.  Dividing both sides by -5, we get (8/5)x -2.  Therefore, y = (8/5)x - 2; the y-intercept is (0,-2).

The equation  -6x-7y=-6   can be solved for its slope in the same manner.
7y = -6x + 6;  then y = (-6/7)x + 6/7.  Its slope is -7/6.  A line perpendicular to this line has slope equal to the negative reciprocal of -7/6,  which is 6/7.

So, using the slope-intercept form, y = mx + b becomes y = (6/7)x -2.