SOLUTION: how do i solve 2x-6y= -12

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Question 123329: how do i solve 2x-6y= -12
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Graphing Linear Equations


2%2Ax-6%2Ay=-12Start with the given equation



-6%2Ay=-12-2%2Ax Subtract 2%2Ax from both sides

y=%28-1%2F6%29%28-12-2%2Ax%29 Multiply both sides by -1%2F6

y=%28-1%2F6%29%28-12%29%2B%281%2F6%29%282%29x%29 Distribute -1%2F6

y=12%2F6%2B%282%2F6%29x Multiply

y=%282%2F6%29%2Ax%2B12%2F6 Rearrange the terms

y=%281%2F3%29%2Ax%2B2 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=1%2F3 (the slope) and b=2 (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%2B2

y=-9%2F3%2B2 Multiply

y=-3%2F3 Add

y=-1 Reduce

So here's one point (-9,-1)





Now lets find another point

Plug in x=-6

y=%281%2F3%29%2A%28-6%29%2B2

y=-6%2F3%2B2 Multiply

y=0%2F3 Add

y=0 Reduce

So here's another point (-6,0). Add this to our graph





Now draw a line through these points

So this is the graph of y=%281%2F3%29%2Ax%2B2 through the points (-9,-1) and (-6,0)


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 (0,2)and the x-intercept is (-6,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=2 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,2).


So we have one point (0,2)






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 (0,2), 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%2B2


So this is the graph of y=%281%2F3%29%2Ax%2B2 through the points (0,2) and (3,3)