What is an equation of the line that is perpendicular to y=−4/5x+3 and passes through the point (4, 12) ?

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: and 12 = 5 + b.  So b = 7.  Rewriting with our new slope and b value, .  And there you go!