SOLUTION: Graph the equation 4x-3y=-12

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Question 119888: Graph the equation 4x-3y=-12
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Solved by pluggable solver: Graphing Linear Equations


4%2Ax-3%2Ay=-12Start with the given equation



-3%2Ay=-12-4%2Ax Subtract 4%2Ax from both sides

y=%28-1%2F3%29%28-12-4%2Ax%29 Multiply both sides by -1%2F3

y=%28-1%2F3%29%28-12%29%2B%281%2F3%29%284%29x%29 Distribute -1%2F3

y=12%2F3%2B%284%2F3%29x Multiply

y=%284%2F3%29%2Ax%2B12%2F3 Rearrange the terms

y=%284%2F3%29%2Ax%2B4 Reduce any fractions

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

So to graph this equation lets plug in some points

Plug in x=-9

y=%284%2F3%29%2A%28-9%29%2B4

y=-36%2F3%2B4 Multiply

y=-24%2F3 Add

y=-8 Reduce

So here's one point (-9,-8)





Now lets find another point

Plug in x=-6

y=%284%2F3%29%2A%28-6%29%2B4

y=-24%2F3%2B4 Multiply

y=-12%2F3 Add

y=-4 Reduce

So here's another point (-6,-4). Add this to our graph





Now draw a line through these points

So this is the graph of y=%284%2F3%29%2Ax%2B4 through the points (-9,-8) and (-6,-4)


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


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



Now draw a line through those points to graph y=%284%2F3%29%2Ax%2B4


So this is the graph of y=%284%2F3%29%2Ax%2B4 through the points (0,4) and (3,8)