# 7-5a Slope Intercept Form

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First of all.  You are MUCH smarter than this program.
What you would normally write as:
y - 3x = 2
The equation maker might write as
-1y + -3x = 2
or occasionally as
-1y + -3x + 0 = 2
That's okay.  We know you're smart enough to ignore the superfluous information.

```When you write an equation as y=mx+b then it is in slope-intercept form.
The number in front of the x is the slope and the b is the y-intercept (the y-value when x is 0)

For instance if y=1/3x - 1 then the slope goes up 1 and right 3.
When you plug in x=0, then y is -1 so the y-intercept is (0,-1)

Similarly if y=-2x + 1 then the slope goes down 2 and right 1 (-2 is the same as -2/1)
The y-intercept is (0,1)

Putting into slope intercept form means solving for y.
For instance if 2x + 3y = -6
Subtract 2x from both sides
3y=-2x-6
divide by 3
y=-2/3x-2  (you could also write as -0.67x-2 but the fraction version is better)

*To find another point that works in Quadrant I or IV
The y-intercept is (0,-2)
Using the slope (-2/3) you must go DOWN 2 and right 3 from (0,-2)
The next point is (0+3,-2-2) or (3,-4)

Similarly if
y=3x+1
The y-intercept is (0,1)
Using the slope (3 or 3/1) you must go UP 3 and right 1 from (0,1)
The next point is (0+1,1+3) or (1,4)

```