What is the equation of a line perpendicular to 4x-7y=23 through (2/3, -4/5) in point-slope form?

Question

I’ve been stuck on this problem for a while. The directions are: find the equation of the line that has the given characteristic. Leave your answer in the form indicated.

Answer 1

First, put the equation into slope-intercept form: y = (4/7)x -(23/7).

 

The slope of the perpendicular, then, is -(7/4).

 

The equation is -(7/4) = [y + (4/5)]/[x - (2/3)]