SOLUTION: how do i graph: 3x-y=6

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Question 236587: how do i graph: 3x-y=6
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
3x-y=6 Start with the given equation.


-y=6-3x Subtract 3x from both sides.


-y=-3x%2B6 Rearrange the terms.


y=%28-3x%2B6%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=%28%28-3%29%2F%28-1%29%29x%2B%286%29%2F%28-1%29 Break up the fraction.


y=3x-6 Reduce.




Looking at y=3x-6 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=3 and the y-intercept is b=-6


Since b=-6 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-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C-6%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-6%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-6%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, this means:

rise%2Frun=3%2F1


which shows us that the rise is 3 and the run is 1. This means that to go from point to point, we can go up 3 and over 1



So starting at , go up 3 units
drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C-6%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-6%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-6%2C.15%29%29%2C%0D%0A++blue%28arc%280%2C-6%2B%283%2F2%29%2C2%2C3%2C90%2C270%29%29%0D%0A%29

and to the right 1 unit to get to the next point
drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++blue%28circle%280%2C-6%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-6%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-6%2C.15%29%29%2C%0D%0A++blue%28circle%281%2C-3%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%281%2C-3%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C-6%2B%283%2F2%29%2C2%2C3%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%281%2F2%29%2C-3%2C1%2C2%2C+180%2C360%29%29%0D%0A%29


Now draw a line through these points to graph y=3x-6

drawing%28500%2C500%2C-10%2C10%2C-10%2C10%2C%0D%0A++grid%281%29%2C%0D%0A++graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C3x-6%29%2C%0D%0A++blue%28circle%280%2C-6%2C.1%29%29%2C%0D%0A++blue%28circle%280%2C-6%2C.12%29%29%2C%0D%0A++blue%28circle%280%2C-6%2C.15%29%29%2C%0D%0A++blue%28circle%281%2C-3%2C.15%2C1.5%29%29%2C%0D%0A++blue%28circle%281%2C-3%2C.1%2C1.5%29%29%2C%0D%0A++blue%28arc%280%2C-6%2B%283%2F2%29%2C2%2C3%2C90%2C270%29%29%2C%0D%0A++blue%28arc%28%281%2F2%29%2C-3%2C1%2C2%2C+180%2C360%29%29%0D%0A%29 So this is the graph of y=3x-6 through the points and