SOLUTION: x + y = 8

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Question 114025: x + y = 8
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to graph this?


Solved by pluggable solver: Graphing Linear Equations


1%2Ax%2B1%2Ay=8Start with the given equation



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

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

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

y=8-%281%29x Multiply

y=-1%2Ax%2B8 Rearrange the terms

y=-1%2Ax%2B8 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-1 (the slope) and b=8 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-1

y=-1%2A%28-1%29%2B8

y=1%2B8 Multiply

y=9 Add

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



drawing%28+600%2C+600%2C+-11%2C10%2C+-2%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+-1%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-1%2C9%2C+.1%2C+1.5+%29+%29%0D%0A++%29

Now lets find another point

Plug in x=0

y=-1%2A%280%29%2B8

y=0%2B8 Multiply

y=8 Add

So here's another point (0,8). Add this to our graph


drawing%28+600%2C+600%2C+-11%2C10%2C+-2%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++blue%28+circle%28+0%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C8%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-1%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-1%2C9%2C+.1%2C+1.5+%29+%29%0D%0A++%29


Now draw a line through these points

drawing%28+600%2C+600%2C+-11%2C10%2C+-2%2C+19%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-11-10%2C-1%2A%28-11-10%29%2B8%2C10%2B10%2C-1%2A%2810%2B10%29%2B8%29%2C%0D%0A++++blue%28+circle%28+0%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C8%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+-1%2C9%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+-1%2C9%2C+.1%2C+1.5+%29+%29%0D%0A++%29 So this is the graph of y=-1%2Ax%2B8 through the points (-1,9) and (0,8)


So from the graph we can see that the slope is -1%2F1 (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 1 units to get to the next point), the y-intercept is (0,8)and the x-intercept is (8,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=8 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,8).


So we have one point (0,8)


drawing%28+600%2C+600%2C+-10%2C11%2C+-3%2C+18%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++%0D%0A++++blue%28+circle%28+0%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C8%2C+.1%2C+1.5+%29+%29%0D%0A++%29



Now since the slope is -1%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,8), we can go down 1 units

drawing%28++600%2C+600%2C+-10%2C11%2C+-3%2C+18%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C8%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+8%2B%28-1%2F2%29%2C+2%2C+-1%2C+90%2C+270+%29+%29%0D%0A++%0D%0A++%29
and to the right 1 units to get to our next point

drawing%28++600%2C+600%2C+-10%2C11%2C+-3%2C+18%2C%0D%0A++++grid%281%29%2C%0D%0A++++blue%28+circle%28+0%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C8%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+1%2C7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+1%2C7%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+8%2B%28-1%2F2%29%2C+2%2C+-1%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%281%2F2%29%2C+7%2C+1%2C+2%2C+0%2C+180+%29+%29%0D%0A++%0D%0A++%29

Now draw a line through those points to graph y=-1%2Ax%2B8


drawing%28+600%2C+600%2C+-10%2C11%2C+-3%2C+18%2C%0D%0A++++grid%28+1+%29%2C%0D%0A++++line%28-10-10%2C-1%2A%28-10-10%29%2B8%2C11%2B10%2C-1%2A%2811%2B10%29%2B8%29%2C%0D%0A++++blue%28+circle%28+1%2C7%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+1%2C7%2C+.1%2C+1.5+%29+%29%2C%0D%0A++++blue%28+circle%28+0%2C8%2C+.15%2C+1.5+%29%29%2C%0D%0A++++blue%28+circle%28+0%2C8%2C+.1%2C+1.5+%29+%29%2C%0D%0A++blue%28+arc%28+0%2C+8%2B%28-1%2F2%29%2C+2%2C+-1%2C+90%2C+270+%29+%29%2C%0D%0A++blue%28+arc%28+%281%2F2%29%2C+7%2C+1%2C+2%2C+0%2C+180+%29+%29%0D%0A++%29 So this is the graph of y=-1%2Ax%2B8 through the points (0,8) and (1,7)