What is an equation of the line that passes through the point (−1,−3) and is parallel to the line 4x-y=2?

 y = 4x + 11

Step-by-step explanation:First, you put the equation into the standard “slope/intercept” form.

4x -y = 2 subtract 4x from both sides ; -y = -4x + 2 Multiply by -1 :

y = 4x - 2

In this standard form we see that the slope of the line (coefficient of x) is 4. ANY line parallel to this one must thus also have a slope of 4.

y = 4x - a (generic)

ANY other combination of slope multiples and constant terms will therefore also be lines parallel to this one. The one that passes through a specific point will simply have a different constant term.

We find this by putting our point value into the equation:

3 = 4(-2) + a ; 3 = -8 + a ; a = 11

Thus, our “parallel line equation” through the point (-2,3) is:

y = 4x + 11