SOLUTION: Graph the following equation by first solving for y. See Example 8 (p 535) in the text for reference. 2x – 3y = 12

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Question 87316: Graph the following equation by first solving for y. See Example 8 (p 535) in the text for reference.
2x – 3y = 12


Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations


2%2Ax-3%2Ay=12Start with the given equation



-3%2Ay=12-2%2Ax Subtract 2%2Ax from both sides

y=%28-1%2F3%29%2812-2%2Ax%29 Multiply both sides by -1%2F3

y=%28-1%2F3%29%2812%29%2B%281%2F3%29%282%29x%29 Distribute -1%2F3

y=-12%2F3%2B%282%2F3%29x Multiply

y=%282%2F3%29%2Ax-12%2F3 Rearrange the terms

y=%282%2F3%29%2Ax-4 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=2%2F3 (the slope) and b=-4 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-6

y=%282%2F3%29%2A%28-6%29-4

y=-12%2F3-4 Multiply

y=-24%2F3 Add

y=-8 Reduce

So here's one point (-6,-8)



drawing%28+600%2C+600%2C+-16%2C7%2C+-18%2C+4%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-6%2C-8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-6%2C-8%2C+.1%2C+1.5+%29+%29%0D%0A++%29

Now lets find another point

Plug in x=-3

y=%282%2F3%29%2A%28-3%29-4

y=-6%2F3-4 Multiply

y=-18%2F3 Add

y=-6 Reduce

So here's another point (-3,-6). Add this to our graph


drawing%28+600%2C+600%2C+-16%2C7%2C+-18%2C+4%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-3%2C-6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-3%2C-6%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-6%2C-8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-6%2C-8%2C+.1%2C+1.5+%29+%29%0D%0A++%29


Now draw a line through these points

drawing%28+600%2C+600%2C+-16%2C7%2C+-18%2C+4%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-16-10%2C0.666666666666667%2A%28-16-10%29%2B-4%2C7%2B10%2C0.666666666666667%2A%287%2B10%29%2B-4%29%2C%0D%0A++++blue%28+circle%28+-3%2C-6%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-3%2C-6%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-6%2C-8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-6%2C-8%2C+.1%2C+1.5+%29+%29%0D%0A++%29 So this is the graph of y=%282%2F3%29%2Ax-4 through the points (-6,-8) and (-3,-6)


So from the graph we can see that the slope is 2%2F3 (which tells us that in order to go from point to point we have to start at one point and go up 2 units and to the right 3 units to get to the next point) the y-intercept is (0,-4)and the x-intercept is (6,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=-4 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-4).


So we have one point (0,-4)


drawing%28+600%2C+600%2C+-10%2C13%2C+-14%2C+8%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-4%2C+.1%2C+1.5+%29+%29%0D%0A++%29



Now since the slope is 2%2F3, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-4), we can go up 2 units

drawing%28++600%2C+600%2C+-10%2C13%2C+-14%2C+8%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-4%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-4%2B%282%2F2%29%2C+2%2C+2%2C+90%2C+270+%29+%29%0D%0A++%0D%0A++%29
and to the right 3 units to get to our next point

drawing%28++600%2C+600%2C+-10%2C13%2C+-14%2C+8%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-4%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+3%2C-2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+3%2C-2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-4%2B%282%2F2%29%2C+2%2C+2%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%283%2F2%29%2C+-2%2C+3%2C+2%2C+180%2C+360+%29+%29%0D%0A++%0D%0A++%29

Now draw a line through those points to graph y=%282%2F3%29%2Ax-4


drawing%28+600%2C+600%2C+-10%2C13%2C+-14%2C+8%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C0.666666666666667%2A%28-10-10%29%2B-4%2C13%2B10%2C0.666666666666667%2A%2813%2B10%29%2B-4%29%2C%0D%0A++++blue%28+circle%28+3%2C-2%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+3%2C-2%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C-4%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C-4%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+-4%2B%282%2F2%29%2C+2%2C+2%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%283%2F2%29%2C+-2%2C+3%2C+2%2C+180%2C+360+%29+%29%0D%0A++%29 So this is the graph of y=%282%2F3%29%2Ax-4 through the points (0,-4) and (3,-2)