Write an equation for the line through P(-2, 2) that is perpendicular to L: y=4-2x.

Question

Be sure to give an explanation as to how you came up with your equation. Thanks!

Answer 1

The equation you seek is y=mx+b. All we have to do is find the correct

values for m (the slope) and b(the y-intercept

First, the slope.

The line we want is perpendicular to y=4-2x. Jiggle y=4-2x around a bit

to read y= -2x+4, and the equation yields its slope. It's the coefficient of

the x term, and is -2. [NOTE! You can only do this if the equation has

+1y all by itself on one side of the = sign]

Lines that are perpendicular have slopes that are the negative reciprocal of

one another. Thus, the line we seek has slope 1/2. 1/2 is the negative

reciprocal of -2.

Our equation is thus y=(1/2)x+b

Our line passes through P(-2,2)

Substitute -2 for x and 2 for y to find b

2=(1/2)(-2)+b

2= -1+b

3=b

Our equation is y=(1/2)x+3, or 2y=x+6