SOLUTION: GRAPH THE FOLLOWING EQUATION BY FIRST SOLVING FOR Y. 2X-3Y=12

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Question 118045: GRAPH THE FOLLOWING EQUATION BY FIRST SOLVING FOR Y.
2X-3Y=12
Answer by jim_thompson5910(35256) 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)





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





Now draw a line through these points

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)






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


and to the right 3 units to get to our next point



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


So this is the graph of y=%282%2F3%29%2Ax-4 through the points (0,-4) and (3,-2)