Question

Which equation represents a line that is parallel to the line whose equation is 3x − 2y = 7? *

Answer 1

Answer:

$y = \frac{3}{2}x - 5$

Explanation:

Given

$3x - 2y = 7$

Required

Select the equation of a line, parallel to this

First, we make y the subject:

$3x - 2y = 7$

Subtract 3x from both sides

$3x-3x - 2y = -3x+7$

$- 2y = -3x+7$

Divide through by -2

$\frac{- 2y}{-2} = \frac{-3x}{-2}+\frac{7}{-2}$

$y = \frac{-3x}{-2}+\frac{7}{-2}$

$y = \frac{3x}{2}-\frac{7}{2}$

$y = \frac{3}{2}x-\frac{7}{2}$

The general form of an equation is:

$y = mx + b$

Where:

$m = slope$

So, we have:

$m = \frac{3}{2}$

For an equation to be parallel, the slope must also be:

$m = \frac{3}{2}$

From the list of given options (see attachment), only

$y = \frac{3}{2}x - 5$

has the same slope.

Hence:

$y = \frac{3}{2}x - 5$ is parallel