Question

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

Answer 1

`y = (3)/(2)x - 5`

Step-by-step 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

`(- 2y)/(-2) = (-3x)/(-2)+(7)/(-2)`

`y = (-3x)/(-2)+(7)/(-2)`

`y = (3x)/(2)-(7)/(2)`

`y = (3)/(2)x-(7)/(2)`

The general form of an equation is:

`y = mx + b`

Where:

`m = slope`

So, we have:

`m = (3)/(2)`

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

`m = (3)/(2)`

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

`y = (3)/(2)x - 5`

has the same slope.

Hence:

`y = (3)/(2)x - 5` is parallel