SOLUTION: hi, can you help me put this in slope form and graph thanks -x - y = -8 2x + 3y = 12

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Question 83605: hi, can you help me put this in slope form and graph thanks
-x - y = -8
2x + 3y = 12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Lets solve for -x+-+y+=+-8
Solved by pluggable solver: Graphing Linear Equations


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



-1%2Ay=-8%2B1%2Ax Add 1%2Ax to both sides

y=%28-1%29%28-8%2B1%2Ax%29 Multiply both sides by -1

y=%28-1%29%28-8%29%2B%281%29%28-1%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)





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





Now draw a line through these points

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)






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


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



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


So this is the graph of y=-1%2Ax%2B8 through the points (0,8) and (1,7)



Lets solve for 2x+%2B+3y+=+12
Solved by pluggable solver: Graphing Linear Equations


2%2Ax%2B3%2Ay=12Start with the given equation



3%2Ay=12-2%2Ax Subtract 2%2Ax from both sides

y=%281%2F3%29%2812-2%2Ax%29 Multiply both sides by 1%2F3

y=%281%2F3%29%2812%29-%281%2F3%29%282%29x%29 Distribute 1%2F3

y=12%2F3-%282%2F3%29x Multiply

y=%28-2%2F3%29%2Ax%2B12%2F3 Rearrange the terms

y=%28-2%2F3%29%2Ax%2B4 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-2%2F3 (the slope) and b=4 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-6

y=%28-2%2F3%29%2A%28-6%29%2B4

y=12%2F3%2B4 Multiply

y=24%2F3 Add

y=8 Reduce

So here's one point (-6,8)





Now lets find another point

Plug in x=-3

y=%28-2%2F3%29%2A%28-3%29%2B4

y=6%2F3%2B4 Multiply

y=18%2F3 Add

y=6 Reduce

So here's another point (-3,6). Add this to our graph





Now draw a line through these points

So this is the graph of y=%28-2%2F3%29%2Ax%2B4 through the points (-6,8) and (-3,6)


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 (0,4)and the x-intercept is (6,0) . 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 -2%2F3, this means that in order to go from point to point we can use the slope to do so. So starting at (0,4), 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%2B4


So this is the graph of y=%28-2%2F3%29%2Ax%2B4 through the points (0,4) and (3,2)