Question

Find the equation of a line parallel to 5x−4y=3 that contains the point (−3,2).

Answer 1

`y=(5)/(4)x+(23)/(4)`

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:

`5x-4y=3\\-4y=-5x+3\\y=(5)/(4)x-(3)/(4)`

So our slope is
`(5)/(4)`

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.

`y=(5)/(4)x+b\\2=(5)/(4)(-3)+b\\8=-15+4b\\23=4b\\b=(23)/(4)`

Now that we know our slope and our b, we can plug those into the formula one last time to get our answer.

`y=(5)/(4)x+(23)/(4)`

This is the answer in slope intercept form