Question

What is an equation of the line that is perpendicular to y=−3/4x+6 and passes through the point (3, 9) ?

Answer 1

Two straight lines perpendicular to each other, the slope of which is negative reciprocal.

y=-4/3x+b

The known points are put into the linear equation

y=-4+b

b=13

y=-4/3x+13

Answer 2

First, put the equation of the line given into slope-intercept form by solving for y. You get y = 2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6.