SOLUTION: how do I draw x+y=11 and 2x+3y=26 onto a graph

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Question 959328: how do I draw x+y=11 and 2x+3y=26 onto a graph
Answer by EdenWolf(517) About Me  (Show Source):
You can put this solution on YOUR website!
1)
Solved by pluggable solver: Graphing Linear Equations
In order to graph y=-1%2Ax%2B11 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=2

y=-1%2A%282%29%2B11

y=-2%2B11 Multiply

y=9 Add

So here's one point (2,9)




Now lets find another point

Plug in x=3

y=-1%2A%283%29%2B11

y=-3%2B11 Multiply

y=8 Add

So here's another point (3,8). Add this to our graph





Now draw a line through these points

So this is the graph of y=-1%2Ax%2B11 through the points (2,9) and (3,8)


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 (0,11)and the x-intercept is (11,0)


We could graph this equation another way. Since b=11 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,11).


So we have one point (0,11)





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 (0,11), 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%2B11


So this is the graph of y=-1%2Ax%2B11 through the points (0,11) and (1,10)

2)
Solved by pluggable solver: Graphing Linear Equations


2%2Ax%2B3%2Ay=26Start with the given equation



3%2Ay=26-2%2Ax Subtract 2%2Ax from both sides

y=%281%2F3%29%2826-2%2Ax%29 Multiply both sides by 1%2F3

y=%281%2F3%29%2826%29-%281%2F3%29%282%29x%29 Distribute 1%2F3

y=26%2F3-%282%2F3%29x Multiply

y=%28-2%2F3%29%2Ax%2B26%2F3 Rearrange the terms

y=%28-2%2F3%29%2Ax%2B26%2F3 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-2%2F3 (the slope) and b=26%2F3 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=1

y=%28-2%2F3%29%2A%281%29%2B26%2F3

y=-2%2F3%2B26%2F3 Multiply

y=24%2F3 Add

y=8 Reduce

So here's one point (1,8)





Now lets find another point

Plug in x=4

y=%28-2%2F3%29%2A%284%29%2B26%2F3

y=-8%2F3%2B26%2F3 Multiply

y=18%2F3 Add

y=6 Reduce

So here's another point (4,6). Add this to our graph





Now draw a line through these points

So this is the graph of y=%28-2%2F3%29%2Ax%2B26%2F3 through the points (1,8) and (4,6)


So from the graph we can see that the slope is -2%2F3 (which tells us that in order to go from point to point we have to start at one point and go down -2 units and to the right 3 units to get to the next point), the y-intercept is (0,8.66666666666667) ,or (0,26%2F3), and the x-intercept is (13,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=26%2F3 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,26%2F3).


So we have one point (0,26%2F3)






Now since the slope is -2%2F3, this means that in order to go from point to point we can use the slope to do so. So starting at (0,26%2F3), we can go down 2 units


and to the right 3 units to get to our next point



Now draw a line through those points to graph y=%28-2%2F3%29%2Ax%2B26%2F3


So this is the graph of y=%28-2%2F3%29%2Ax%2B26%2F3 through the points (0,8.66666666666667) and (3,6.66666666666667)