Question

A line has a slope of –5 and a y-intercept of (0, 3). What is the equation of the line that is perpendicular to the first line and passes through the point (3, 2)?

Answer 1

If two lines are perpendicular, their slopes are negative reciprocals of one another. Applying this here: If the new line is to be perpendicular to the one whose slope is -5, then the new line must have the slope +1/5 (the negative reciprocal of -5).

The new line passes through (3,2). Let's take all the info we have and solve for the y-intercept, b, of the new line:

general slope-intercept formula for a str. line is y=mx+b.

Here we have x=3 and y=2, as well as m=1/5.

Then 2 = (1/5)(3)+b

Clear out the fractions by multiplying all 3 terms by 5: 5(2) = 5(1/5)(3) + b.

Then 10 = 3 + b; b=7.

The equation of the new line is then y=(1/5)x+7.