The slope of the given line is -4/5. The line perpendicular to that line will have a slope that is the opposite reciprocal. In other words, the perpendicular slope will be 5/4. If it passes through (4, 12), we have an x and a y value to use in y=mx+b. y is 12, x is 4, and we have a slope of 5/4. Filling in accordingly: [tex]12= \frac{5}{4}(4)+b [/tex] and 12 = 5 + b. So b = 7. Rewriting with our new slope and b value, [tex]y= \frac{5}{4}x+7 [/tex]. And there you go!
