Write a slope intercept equation for a line passing through the point (5,-3) that is parallel to the line 5x+7y=8. then write a second equation for a line passing through the point (5,-3) that is perpendicular to the line 5x+7y=8. so

We're starting with the line

All the lines parallel to it will be of the form

and when our intersection point is (5,-3) the constant must be

That's the answer but we have to turn this into slope intercept form so we solve for y:

y = (-5/7)x + 4/7

For perpendicular lines, we swap the coefficients on x and y, negating one:

Again the point gives the constant:

Solve for y for slope/intercept:

[tex]y = \frac 7 5  x - 10

y = (7/5) x - 10

Let's check with a nice plot:

i think the answer would be c