Hello, Bee!
To answer this question, you need to recall that perpendicular lines have slopes that are opposite signs and reciprocals of each other. You'd also need to know that reciprocals are essentially flipped fractions of each other (EX: 3/4 and 4/3 are reciprocals).
STEP ONE: Change the equation into slope-intercept form (if not already).
A. This equation is already in slope-intercept form.
STEP TWO: Identify the slope.
A. Recall that slope-intercept form is y=mx + b where m is slope and b is the y-intercept.
B. This means that the number in front of x is the slope, which is 2/3.
STEP THREE: Find the reciprocal of the slope and make it negative.
A. The slope was 2/3.
B. To find the reciprocal, we just flip this fraction, and it becomes 3/2.
C. We also must make the slope negative, so it'd be -3/2.
STEP FOUR: Identity the answer choice with the correct slope by changing the answer choices into slope-intercept form (if needed).
A. All of the answer choices are already in slope-intercept form.
B. We pay attention to the number in front of the "x" to identify the slope.
C. Only answer choice D has -3/2 as the slope.
I hope this helps!
-Leah
