SOLUTION: Graph by first solving for y. x – 3y = 9

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Question 114744: Graph by first solving for y.
x – 3y = 9

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations


1%2Ax-3%2Ay=9Start with the given equation



-3%2Ay=9-1%2Ax Subtract 1%2Ax from both sides

y=%28-1%2F3%29%289-1%2Ax%29 Multiply both sides by -1%2F3

y=%28-1%2F3%29%289%29%2B%281%2F3%29%281%29x%29 Distribute -1%2F3

y=-9%2F3%2B%281%2F3%29x Multiply

y=%281%2F3%29%2Ax-9%2F3 Rearrange the terms

y=%281%2F3%29%2Ax-3 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=1%2F3 (the slope) and b=-3 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-9

y=%281%2F3%29%2A%28-9%29-3

y=-9%2F3-3 Multiply

y=-18%2F3 Add

y=-6 Reduce

So here's one point (-9,-6)





Now lets find another point

Plug in x=-6

y=%281%2F3%29%2A%28-6%29-3

y=-6%2F3-3 Multiply

y=-15%2F3 Add

y=-5 Reduce

So here's another point (-6,-5). Add this to our graph





Now draw a line through these points

So this is the graph of y=%281%2F3%29%2Ax-3 through the points (-9,-6) and (-6,-5)


So from the graph we can see that the slope is 1%2F3 (which tells us that in order to go from point to point we have to start at one point and go up 1 units and to the right 3 units to get to the next point) the y-intercept is (0,-3)and the x-intercept is (9,0) . 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 1%2F3, 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 up 1 units


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



Now draw a line through those points to graph y=%281%2F3%29%2Ax-3


So this is the graph of y=%281%2F3%29%2Ax-3 through the points (0,-3) and (3,-2)