SOLUTION: What is the graph of x + y = 1 ? Thank you

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Question 118744: What is the graph of x + y = 1 ?
Thank you
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%2B1%2Ay=1Start with the given equation



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

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

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

y=1-%281%29x Multiply

y=-1%2Ax%2B1 Rearrange the terms

y=-1%2Ax%2B1 Reduce any fractions

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

So to graph this equation lets plug in some points

Plug in x=-8

y=-1%2A%28-8%29%2B1

y=8%2B1 Multiply

y=9 Add

So here's one point (-8,9)





Now lets find another point

Plug in x=-7

y=-1%2A%28-7%29%2B1

y=7%2B1 Multiply

y=8 Add

So here's another point (-7,8). Add this to our graph





Now draw a line through these points

So this is the graph of y=-1%2Ax%2B1 through the points (-8,9) and (-7,8)


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 (0,1)and the x-intercept is (1,0) . 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%2F1, 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 down 1 units


and to the right 1 units to get to our next point



Now draw a line through those points to graph y=-1%2Ax%2B1


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