SOLUTION: how would i graph this equation... x-2y=-2

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Question 765841: how would i graph this equation... x-2y=-2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Graphing Linear Equations


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



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

y=%28-1%2F2%29%28-2-1%2Ax%29 Multiply both sides by -1%2F2

y=%28-1%2F2%29%28-2%29%2B%281%2F2%29%281%29x%29 Distribute -1%2F2

y=2%2F2%2B%281%2F2%29x Multiply

y=%281%2F2%29%2Ax%2B2%2F2 Rearrange the terms

y=%281%2F2%29%2Ax%2B1 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=1%2F2 (the slope) and b=1 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-8

y=%281%2F2%29%2A%28-8%29%2B1

y=-8%2F2%2B1 Multiply

y=-6%2F2 Add

y=-3 Reduce

So here's one point (-8,-3)





Now lets find another point

Plug in x=-6

y=%281%2F2%29%2A%28-6%29%2B1

y=-6%2F2%2B1 Multiply

y=-4%2F2 Add

y=-2 Reduce

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





Now draw a line through these points

So this is the graph of y=%281%2F2%29%2Ax%2B1 through the points (-8,-3) and (-6,-2)


So from the graph we can see that the slope is 1%2F2 (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 2 units to get to the next point) the y-intercept is (0,1)and the x-intercept is (-2,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=1 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,1).


So we have one point (0,1)






Now since the slope is 1%2F2, this means that in order to go from point to point we can use the slope to do so. So starting at (0,1), we can go up 1 units


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



Now draw a line through those points to graph y=%281%2F2%29%2Ax%2B1


So this is the graph of y=%281%2F2%29%2Ax%2B1 through the points (0,1) and (2,2)