A line is parallel to y=-3x+2 and intersects the point (4, 3). Why is the equation of this parallel line?

Answer 1

A line is parallel to another line when they have the same slope. Notice that the equation of the original line is in the form of y = mx + b, where m denotes the slope of the line. The slope of the line we are trying to solve for will therefore have a slope of -3.

In order to make sure that the slope of the line goes through the point (4,3), we can just use point slope form to solve for our line.

The equation of the parallel line is therefore:

y - 3 = -3(x-4)

y-3 = -3x + 12

y = -3x + 15

Answer 2

m = -3

The slope of the line that we are looking for is the same as the given line because they are parallel.

at (4,3)

Using y=mx +b

3 = -3(4) +b

-b = -12 -3

-b = -15

b = 15

Therefore the equation of the line is:

y = -3x + 15