SOLUTION: Graph 3x-2y=-18

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Question 139503: Graph
3x-2y=-18
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

3x-2y=-18 Start with the given equation


-2y=-18-3x Subtract 3+x from both sides


-2y=-3x-18 Rearrange the equation


y=%28-3x-18%29%2F%28-2%29 Divide both sides by -2


y=%28-3%2F-2%29x%2B%28-18%29%2F%28-2%29 Break up the fraction


y=%283%2F2%29x%2B9 Reduce




Looking at y=%283%2F2%29x%2B9 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=3%2F2 and the y-intercept is b=9


Since b=9 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point

drawing%28500%2C500%2C-10%2C10%2C-5%2C15%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C9%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C9%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C9%2C.15%29%29%0D%0A%29


Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is 3%2F2, this means:

rise%2Frun=3%2F2


which shows us that the rise is 3 and the run is 2. This means that to go from point to point, we can go up 3 and over 2



So starting at , go up 3 units
drawing%28500%2C500%2C-10%2C10%2C-5%2C15%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C9%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C9%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C9%2C.15%29%29%2C%0D%0A++blue%28arc%280%2C9%2B%283%2F2%29%2C2%2C3%2C90%2C270%29%29%0D%0A%29

and to the right 2 units to get to the next point
drawing%28500%2C500%2C-10%2C10%2C-5%2C15%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C9%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C9%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C9%2C.15%29%29%2C%0D%0A++blue%28circle%282%2C12%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%282%2C12%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C9%2B%283%2F2%29%2C2%2C3%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%282%2F2%29%2C12%2C2%2C2%2C+180%2C360%29%29%0D%0A%29


Now draw a line through these points to graph y=%283%2F2%29x%2B9

drawing%28500%2C500%2C-10%2C10%2C-5%2C15%2C%0D%0A++grid%281%29%2C%0D%0A++graph%28500%2C500%2C-10%2C10%2C-5%2C15%2C%283%2F2%29x%2B9%29%2C%0D%0A++blue%28circle%280%2C9%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C9%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C9%2C.15%29%29%2C%0D%0A++blue%28circle%282%2C12%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%282%2C12%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C9%2B%283%2F2%29%2C2%2C3%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%282%2F2%29%2C12%2C2%2C2%2C+180%2C360%29%29%0D%0A%29 So this is the graph of y=%283%2F2%29x%2B9 through the points and