Answer:
[tex]y = \frac{3}{2}x - 5[/tex]
Explanation:
Given
[tex]3x - 2y = 7[/tex]
Required
Select the equation of a line, parallel to this
First, we make y the subject:
[tex]3x - 2y = 7[/tex]
Subtract 3x from both sides
[tex]3x-3x - 2y = -3x+7[/tex]
[tex]- 2y = -3x+7[/tex]
Divide through by -2
[tex]\frac{- 2y}{-2} = \frac{-3x}{-2}+\frac{7}{-2}[/tex]
[tex]y = \frac{-3x}{-2}+\frac{7}{-2}[/tex]
[tex]y = \frac{3x}{2}-\frac{7}{2}[/tex]
[tex]y = \frac{3}{2}x-\frac{7}{2}[/tex]
The general form of an equation is:
[tex]y = mx + b[/tex]
Where:
[tex]m = slope[/tex]
So, we have:
[tex]m = \frac{3}{2}[/tex]
For an equation to be parallel, the slope must also be:
[tex]m = \frac{3}{2}[/tex]
From the list of given options (see attachment), only
[tex]y = \frac{3}{2}x - 5[/tex]
has the same slope.
Hence:
[tex]y = \frac{3}{2}x - 5[/tex] is parallel
