Answer:
[tex]y=\frac{5}{4}x+\frac{23}{4}[/tex]
Step-by-step explanation:
To find a line that is parallel, we need to find a line with the same slope. Remember the formula y = mx + b? We need to put this equation into this form to find m, which is the slope.
In other words, let's solve for y:
[tex]5x-4y=3\\-4y=-5x+3\\y=\frac{5}{4}x-\frac{3}{4}[/tex]
So our slope is [tex]\frac{5}{4}[/tex]
Now we need to use that equation again to find b (the y-intercept) of the different equation. To do this, we plug in (-3,2) for x and y in that formula. Remember, it has the same slope so we don't need to worry about finding that again.
[tex]y=\frac{5}{4}x+b\\2=\frac{5}{4}(-3)+b\\8=-15+4b\\23=4b\\b=\frac{23}{4}[/tex]
Now that we know our slope and our b, we can plug those into the formula one last time to get our answer.
[tex]y=\frac{5}{4}x+\frac{23}{4}[/tex]
This is the answer in slope intercept form
