Write the slope-intercept form of the equation of the line through (-4,-2) and parallel to y=x+3

Answer 1

y = mx + b

Parallel lines have equal slopes, so

m = 1

y = x + b

Use the given point to find b.

-2 = -4 + b

b = 2

y = x + 2

Answer 2

For a line to be parallel to another line, their slopes must be the same. The slope of y=x+3 is 1 so the slope of the new line must also be 1. The 1 comes from the slope-intercept form,, y=mx+b , where m is the slope. We are trying to find this form for the new line. We determined that the slope,m, is 1 for this line as well.

So far we have, y=1x+b and we are given that this line passes through (-4,-2) so (-4,-2) must be a solution to the equation. Therefore, we can plug in -4 in x and -2 in y and then solve for b which is the y-intercept of the line.

So we have: -2 = 1(-4)+b

-2 = -4 + b add 4 to both sides

2 = b

So we have determined m = 1 and b = 2 so the the slope-intercept form (y = mx+ b) of this line is y = x+2