Carcass wrote:
In the xy-plane, what is the slope of the line whose equation is 3x - 2y = 8 ?
A) -4
B)\(-\frac{8}{3}\)
C) \(\frac{2}{3}\)
D) \(\frac{3}{2}\)
E) 2
I'd typically use Sandy's approach of rewriting the equation in slope y-intercept form. It's at least three times as fast, since you can practically rewrite the equation in your head.
However, as a "fun" exercise, let's examine an alternate approach that we might use to our advantage in a different question in which Sandy's chosen strategy doesn't apply.
The strategy is to find two points ON the line and then find the slope between those two points.
GIVEN: 3x - 2y = 8
If x = 0, we get: 3(0) - 2y = 8
Solve for y to get y = -4
So, the point
(0, -4) lies on the line.
Find a second point on the line.
GIVEN: 3x - 2y = 8
If x = 2, we get: 3(2) - 2y = 8
Solve for y to get y = -1
So, the point
(2, -1) lies on the line.
Now use the
slope formula to find the slope between
(0, -4) and
(2, -1)Slope = [(-4) - (-1)]/(0 - 2)
= (-3)/(-2)
= 3/2
Answer: D
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep