Question

What is the equation of the line in slope-intercept form that is perpendicular to the line y =-2x-1 and passes through the point (2,1)?

Answer 1

`y=(1)/(2)x -1`

Explanation:

Perpendicular lines have slopes which are negative reciprocals of each other. The slope of the line y=-2x-1 is -2. The slope perpendicular to it is 1/2.

Using m=1/2, substitute it and (2,1) into the point slope form and simplify to find the y-intercept.

`y-y_1 = m(x-x_1)\\y-1=(1)/(2)(x-2)\\y-1=(1)/(2)(x-4)\\y-1=(1)/(2)x-2\\y=(1)/(2)x-1`