SOLUTION: graph x+2y=8

Algebra ->  Graphs -> SOLUTION: graph x+2y=8      Log On


   

Question 228672: graph x+2y=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


1%2Ax%2B2%2Ay=8Start with the given equation



2%2Ay=8-1%2Ax Subtract 1%2Ax from both sides

y=%281%2F2%29%288-1%2Ax%29 Multiply both sides by 1%2F2

y=%281%2F2%29%288%29-%281%2F2%29%281%29x%29 Distribute 1%2F2

y=8%2F2-%281%2F2%29x Multiply

y=%28-1%2F2%29%2Ax%2B8%2F2 Rearrange the terms

y=%28-1%2F2%29%2Ax%2B4 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-1%2F2 (the slope) and b=4 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-8

y=%28-1%2F2%29%2A%28-8%29%2B4

y=8%2F2%2B4 Multiply

y=16%2F2 Add

y=8 Reduce

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





Now lets find another point

Plug in x=-6

y=%28-1%2F2%29%2A%28-6%29%2B4

y=6%2F2%2B4 Multiply

y=14%2F2 Add

y=7 Reduce

So here's another point (-6,7). Add this to our graph





Now draw a line through these points

So this is the graph of y=%28-1%2F2%29%2Ax%2B4 through the points (-8,8) and (-6,7)


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 down -1 units and to the right 2 units to get to the next point), the y-intercept is (0,4)and the x-intercept is (8,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=4 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,4).


So we have one point (0,4)






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 (0,4), we can go down 1 units


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



Now draw a line through those points to graph y=%28-1%2F2%29%2Ax%2B4


So this is the graph of y=%28-1%2F2%29%2Ax%2B4 through the points (0,4) and (2,3)