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Slopes and Equations of Parallel Lines

Q: Please show me how to write an equation that is the slope-intercept form of the equation of the line that passes through (1,2) and is parallel to 4x-2y=6

A: This looks hard at first, but it’s actually not too bad.

First, let’s rearrange the 4x-2y=6 line so that it’s in slope-intercept form, y=mx+b

4x-2y=6
4x-6=2y

Divide both sides by 2:

4x/2 -6/2 = y
2x – 3 = y
y=2x -3

So the slope of this line is 2, because m=2.

If a line is parallel to it, it must have the exact same slope. Parallel lines always have identical slopes. We know that this second line passes through the point (1,2), which means that x=1 and y=2. We already know that m=2, so put it all into the equation of a line and solve for b:

y=mx+b
2=2(1)+b
2=2+b
2-2=b
b=0

So the y-intercept is zero.

The equation of the line is:

y=2x

To see a graph of this line on Wolfram Alpha, click here.