Which of the following could be the equation of a line parallel to the line 3x + 2y = 8?

[BTGmoderatorLU]

Source: Manhattan Prep

Which of the following could be the equation of a line parallel to the line 3x + 2y = 8?

A. \(y=\dfrac{2}{3}x+7\)

B. \(y=-\dfrac{2}{3}x+7\)

C. \(y=\dfrac{3}{2}x+7\)

D. \(y=-\dfrac{3}{2}x+7\)

E. \(y=\dfrac{3}{2}x-7\)

The OA is D

[Scott@TargetTestPrep]

Source: Manhattan Prep

Which of the following could be the equation of a line parallel to the line 3x + 2y = 8?

A. \(y=\dfrac{2}{3}x+7\)

B. \(y=-\dfrac{2}{3}x+7\)

C. \(y=\dfrac{3}{2}x+7\)

D. \(y=-\dfrac{3}{2}x+7\)

E. \(y=\dfrac{3}{2}x-7\)

The OA is D

Solution:

If two lines are parallel, then they have the same slope. So let’s rewrite the given equation in slope-intercept form:

3x + 2y = 8

2y = -3x + 8

y = (-3/2)x + 4

We see that the slope of the line is -3/2 and the only answer choice that also has a slope of -3/2 is choice D.

Answer: D