SOLUTION: graph the linear equations -2x+16y=-8

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Question 116722: graph the linear equations
-2x+16y=-8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations


-2%2Ax%2B16%2Ay=-8Start with the given equation



16%2Ay=-8%2B2%2Ax Add 2%2Ax to both sides

y=%281%2F16%29%28-8%2B2%2Ax%29 Multiply both sides by 1%2F16

y=%281%2F16%29%28-8%29-%281%2F16%29%28-2%29x%29 Distribute 1%2F16

y=-8%2F16%2B%282%2F16%29x Multiply

y=%282%2F16%29%2Ax-8%2F16 Rearrange the terms

y=%281%2F8%29%2Ax-1%2F2 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=1%2F8 (the slope) and b=-1%2F2 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-4

y=%281%2F8%29%2A%28-4%29-1%2F2

y=-4%2F8-1%2F2 Multiply

y=-8%2F8 Add

y=-1 Reduce

So here's one point (-4,-1)





Now lets find another point

Plug in x=4

y=%281%2F8%29%2A%284%29-1%2F2

y=4%2F8-1%2F2 Multiply

y=0%2F8 Add

y=0 Reduce

So here's another point (4,0). Add this to our graph





Now draw a line through these points

So this is the graph of y=%281%2F8%29%2Ax-1%2F2 through the points (-4,-1) and (4,0)


So from the graph we can see that the slope is 1%2F8 (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 8 units to get to the next point) the y-intercept is (0,-0.5) ,or (0,-1%2F2), and the x-intercept is (4,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=-1%2F2 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-1%2F2).


So we have one point (0,-1%2F2)






Now since the slope is 1%2F8, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-1%2F2), we can go up 1 units


and to the right 8 units to get to our next point



Now draw a line through those points to graph y=%281%2F8%29%2Ax-1%2F2


So this is the graph of y=%281%2F8%29%2Ax-1%2F2 through the points (0,-0.5) and (8,0.5)