SOLUTION: can you please help again, put each in slope form and show me 3 graph. Thanks so much. I'm not understanding how you get those points -x+3y=-9 3x-2y=6 4x-3y=6

Algebra ->  Linear-equations -> SOLUTION: can you please help again, put each in slope form and show me 3 graph. Thanks so much. I'm not understanding how you get those points -x+3y=-9 3x-2y=6 4x-3y=6      Log On


   

Question 83757: can you please help again, put each in slope form and show me 3 graph. Thanks so much. I'm not understanding how you get those points
-x+3y=-9
3x-2y=6
4x-3y=6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Lets put -x%2B3y=-9 into slope intercept form

Solved by pluggable solver: Graphing Linear Equations


-1%2Ax%2B3%2Ay=-9Start with the given equation



3%2Ay=-9%2B1%2Ax Add 1%2Ax to both sides

y=%281%2F3%29%28-9%2B1%2Ax%29 Multiply both sides by 1%2F3

y=%281%2F3%29%28-9%29-%281%2F3%29%28-1%29x%29 Distribute 1%2F3

y=-9%2F3%2B%281%2F3%29x Multiply

y=%281%2F3%29%2Ax-9%2F3 Rearrange the terms

y=%281%2F3%29%2Ax-3 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=1%2F3 (the slope) and b=-3 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-9

y=%281%2F3%29%2A%28-9%29-3

y=-9%2F3-3 Multiply

y=-18%2F3 Add

y=-6 Reduce

So here's one point (-9,-6)





Now lets find another point

Plug in x=-6

y=%281%2F3%29%2A%28-6%29-3

y=-6%2F3-3 Multiply

y=-15%2F3 Add

y=-5 Reduce

So here's another point (-6,-5). Add this to our graph





Now draw a line through these points

So this is the graph of y=%281%2F3%29%2Ax-3 through the points (-9,-6) and (-6,-5)


So from the graph we can see that the slope is 1%2F3 (which tells us that in order to go from point to point we have to start at one point and go up 1 units and to the right 3 units to get to the next point) the y-intercept is (0,-3)and the x-intercept is (9,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=-3 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-3).


So we have one point (0,-3)






Now since the slope is 1%2F3, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-3), we can go up 1 units


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



Now draw a line through those points to graph y=%281%2F3%29%2Ax-3


So this is the graph of y=%281%2F3%29%2Ax-3 through the points (0,-3) and (3,-2)



Lets put 3x-2y=6 into slope intercept form

Solved by pluggable solver: Graphing Linear Equations


3%2Ax-2%2Ay=6Start with the given equation



-2%2Ay=6-3%2Ax Subtract 3%2Ax from both sides

y=%28-1%2F2%29%286-3%2Ax%29 Multiply both sides by -1%2F2

y=%28-1%2F2%29%286%29%2B%281%2F2%29%283%29x%29 Distribute -1%2F2

y=-6%2F2%2B%283%2F2%29x Multiply

y=%283%2F2%29%2Ax-6%2F2 Rearrange the terms

y=%283%2F2%29%2Ax-3 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=3%2F2 (the slope) and b=-3 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-4

y=%283%2F2%29%2A%28-4%29-3

y=-12%2F2-3 Multiply

y=-18%2F2 Add

y=-9 Reduce

So here's one point (-4,-9)





Now lets find another point

Plug in x=-2

y=%283%2F2%29%2A%28-2%29-3

y=-6%2F2-3 Multiply

y=-12%2F2 Add

y=-6 Reduce

So here's another point (-2,-6). Add this to our graph





Now draw a line through these points

So this is the graph of y=%283%2F2%29%2Ax-3 through the points (-4,-9) and (-2,-6)


So from the graph we can see that the slope is 3%2F2 (which tells us that in order to go from point to point we have to start at one point and go up 3 units and to the right 2 units to get to the next point) the y-intercept is (0,-3)and the x-intercept is (2,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=-3 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-3).


So we have one point (0,-3)






Now since the slope is 3%2F2, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-3), we can go up 3 units


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



Now draw a line through those points to graph y=%283%2F2%29%2Ax-3


So this is the graph of y=%283%2F2%29%2Ax-3 through the points (0,-3) and (2,0)




Lets put 4x-3y=6 into slope intercept form

Solved by pluggable solver: Graphing Linear Equations


4%2Ax-3%2Ay=6Start with the given equation



-3%2Ay=6-4%2Ax Subtract 4%2Ax from both sides

y=%28-1%2F3%29%286-4%2Ax%29 Multiply both sides by -1%2F3

y=%28-1%2F3%29%286%29%2B%281%2F3%29%284%29x%29 Distribute -1%2F3

y=-6%2F3%2B%284%2F3%29x Multiply

y=%284%2F3%29%2Ax-6%2F3 Rearrange the terms

y=%284%2F3%29%2Ax-2 Reduce any fractions

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

So to graph this equation lets plug in some points

Plug in x=-3

y=%284%2F3%29%2A%28-3%29-2

y=-12%2F3-2 Multiply

y=-18%2F3 Add

y=-6 Reduce

So here's one point (-3,-6)





Now lets find another point

Plug in x=0

y=%284%2F3%29%2A%280%29-2

y=0%2F3-2 Multiply

y=-6%2F3 Add

y=-2 Reduce

So here's another point (0,-2). Add this to our graph





Now draw a line through these points

So this is the graph of y=%284%2F3%29%2Ax-2 through the points (-3,-6) and (0,-2)


So from the graph we can see that the slope is 4%2F3 (which tells us that in order to go from point to point we have to start at one point and go up 4 units and to the right 3 units to get to the next point) the y-intercept is (0,-2)and the x-intercept is (1.5,0) ,or (3%2F2,0) . So all of this information verifies our graph.


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


So we have one point (0,-2)






Now since the slope is 4%2F3, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-2), we can go up 4 units


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



Now draw a line through those points to graph y=%284%2F3%29%2Ax-2


So this is the graph of y=%284%2F3%29%2Ax-2 through the points (0,-2) and (3,2)