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

Hey!

So the first thing that we can notice is that we are given the equation of a line parallel to one that we need to find. Parallel lines always have the same slope. Since we are not given the equation in slope-intercept form we can't fine the slope by just looking at it. The first thing we need to do is change it to slope-intercept form:

-3x + 4y = 4

4y = 3x + 4

y = (3/4)x + 1

Now that we know the slope of the line that we were given, we also know the slope of the line we need to find (the slope is 3/4). Using this and the point we are given we can find the y-intercept or b:

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

0 = 3 + b

-3 = b

Knowing both the y-intercept and the slope we can get the equation of the line as:

y = (3/4)x - 3

quit

step-by-step explanation: