Question

Which of the following equations represents a line that is parallel to the line with equation y = 3/2*x-7/4?

(A) 6x+4y=8
(B) -6x + 4y = 11
(C) x-2y=-4
(D) 3x+2y=7​

Answer 1

(B) -6x + 4y = 11

Explanation:

Two lines are parallel if they have the same slope

In the line equation, y = mx + b, m = slope

For y = 3/2*x - 7/4, slope = 3/2

(B) can be written as

4y = 6x +11

Dividing by 4 on both sides gives y = 6/4*x + 11/4 which is 3/2*x + 11/4 so the coefficient of x (the slope) is 3/2 which is the slope of the line in the question

Using same strategies for the other lines, you will see
(A) has slope -3/2

(C) has slope 1/2

(D) has slope -3/2