Write the slope-intercept form of the equation of the line through (1,3) and parallel to y=2x-3

Answer 1

For a line to be parallel to another line, their slopes must be the same. The slope of y=2x-3 is 2 so the slope of the new line must also be 2. The 2 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 2 for this line as well.

So far we have, y=2x+b and we are given that this line passes through (1,3) so (1,3) must be a solution to the equation. Therefore, we can plug in 1 in x and 3 in y and then solve for b which is the y-intercept of the line.

So we have: 3 = 2(1)+b

3 = 2 + b subtract 2 from both sides

1 = b

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