SOLUTION: Graph 3x+2y=6

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Question 117823: Graph 3x+2y=6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations


3%2Ax%2B2%2Ay=6Start with the given equation



2%2Ay=6-3%2Ax Subtract 3%2Ax from both sides

y=%281%2F2%29%286-3%2Ax%29 Multiply both sides by 1%2F2

y=%281%2F2%29%286%29-%281%2F2%29%283%29x%29 Distribute 1%2F2

y=6%2F2-%283%2F2%29x Multiply

y=%28-3%2F2%29%2Ax%2B6%2F2 Rearrange the terms

y=%28-3%2F2%29%2Ax%2B3 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-3%2F2 (the slope) and b=3 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-4

y=%28-3%2F2%29%2A%28-4%29%2B3

y=12%2F2%2B3 Multiply

y=18%2F2 Add

y=9 Reduce

So here's one point (-4,9)





Now lets find another point

Plug in x=-2

y=%28-3%2F2%29%2A%28-2%29%2B3

y=6%2F2%2B3 Multiply

y=12%2F2 Add

y=6 Reduce

So here's another point (-2,6). Add this to our graph





Now draw a line through these points

So this is the graph of y=%28-3%2F2%29%2Ax%2B3 through the points (-4,9) and (-2,6)


So from the graph we can see that the slope is -3%2F2 (which tells us that in order to go from point to point we have to start at one point and go down -3 units and to the right 2 units to get to the next point), the y-intercept is (0,3)and the x-intercept is (2,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=3 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,3).


So we have one point (0,3)






Now since the slope is -3%2F2, this means that in order to go from point to point we can use the slope to do so. So starting at (0,3), we can go down 3 units


and to the right 2 units to get to our next point



Now draw a line through those points to graph y=%28-3%2F2%29%2Ax%2B3


So this is the graph of y=%28-3%2F2%29%2Ax%2B3 through the points (0,3) and (2,0)