Answer:
[tex]D.\ y = \frac{5}{2} - 4[/tex]
Step-by-step explanation:
Given
[tex]5x - 2y = 18[/tex]
Required
Determine parallel line
First, we need to convert the equation to slope intercept form
[tex]5x - 2y = 18[/tex]
[tex]- 2y = 18 - 5x[/tex]
Make y the subject:
[tex]y = \frac{18}{-2} - \frac{5x}{-2}[/tex]
[tex]y = -9 + \frac{5}{2}x[/tex]
[tex]y = \frac{5}{2}x - 9[/tex]
The general form of an equation is:
[tex]y=mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m = \frac{5}{2}[/tex]
From the condition of parallel equation.
A parallel equation will have an equal slope of [tex]\frac{5}{2}[/tex]
From the list of given options, option D has a slope of [tex]\frac{5}{2}[/tex]
