Aline 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)?

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.