How do you write the slope-intercept form of the equation of the line perpendicular to the graph of #y=-3/2x-7# that passes through (3, -2)?

1 Answer
Mar 24, 2018

Answer:

#y=2/3x-4#

Explanation:

Slope-intercept form: y=mx+b where m is the slope and b is the y-intercept

First, let's find the slope of the equation. It is perpendicular to #y=-3/2x-7#.

Perpendicular slopes are always opposite reciprocals of one another.

Opposites: positive vs. negative (-3 and 3 are opposites)

Reciprocals: numbers that multiply to 1 (#1/3# and #3# are reciprocals), flip the numerator and denominator of a number to find its reciprocal

Opposite of #-3/2# is (positive) #3/2#

Reciprocal of #-3/2# is #-2/3#

Opposite (positive) reciprocal of #-3/2# is #2/3#

So far our equation is #y=2/3x+b#. We need to find the y-intercept.

Plug in the point that lies on this equation (3, -2)

#-2=2/3*3+b#

#-2=2+b#

#b=-4 rarr# This is the y-intercept

The equation is #y=2/3x-4#