Question

What is the equation of a line that is parallel to −3x+4y=4 and passes through the point (4, 0) ?

Answer 1

Hey!

So the first thing you want to do is put the line that you are given in slope-intercept form so that we can find the slope of the line parallel to it. Two lines that are parallel will always have the same slope. So lets start by changing the format of the equation:

-3x + 4y = 4

4y = 3x + 4

y = (3/4)x + 1

Now that we have the equation in slope-intercept form we can see that the slope of the line parallel to this is 3/4. So we already know the slope of the line and a point on the line. We can now plug this point into the equation y = mx + b. Since we also know the slope we can plug that in as well.

0 = (3/4)(4) + b

0 = 3 + b

-3 = b

Now that we know the y-intercept you can plug that and the slope into the y=mx + b equation to get your answer:

y = (3/4)x - 3