Question

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

Answer 1

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:
`12= (5)/(4)(4)+b` and 12 = 5 + b. So b = 7. Rewriting with our new slope and b value,
`y= (5)/(4)x+7`. And there you go!