**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.

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