SOLUTION: can you please graph and put into slope form. I need the y intercept and then the slope point Thanks -3x + 4y = 2 -2x - y = -3

Algebra ->  Linear-equations -> SOLUTION: can you please graph and put into slope form. I need the y intercept and then the slope point Thanks -3x + 4y = 2 -2x - y = -3      Log On


   

Question 83580: can you please graph and put into slope form. I need the y intercept and then the slope point Thanks
-3x + 4y = 2
-2x - y = -3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Lets solve for -3x+%2B+4y+=+2
Solved by pluggable solver: Graphing Linear Equations


-3%2Ax%2B4%2Ay=2Start with the given equation



4%2Ay=2%2B3%2Ax Add 3%2Ax to both sides

y=%281%2F4%29%282%2B3%2Ax%29 Multiply both sides by 1%2F4

y=%281%2F4%29%282%29-%281%2F4%29%28-3%29x%29 Distribute 1%2F4

y=2%2F4%2B%283%2F4%29x Multiply

y=%283%2F4%29%2Ax%2B2%2F4 Rearrange the terms

y=%283%2F4%29%2Ax%2B1%2F2 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=3%2F4 (the slope) and b=1%2F2 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-6

y=%283%2F4%29%2A%28-6%29%2B1%2F2

y=-18%2F4%2B1%2F2 Multiply

y=-16%2F4 Add

y=-4 Reduce

So here's one point (-6,-4)





Now lets find another point

Plug in x=-2

y=%283%2F4%29%2A%28-2%29%2B1%2F2

y=-6%2F4%2B1%2F2 Multiply

y=-4%2F4 Add

y=-1 Reduce

So here's another point (-2,-1). Add this to our graph





Now draw a line through these points

So this is the graph of y=%283%2F4%29%2Ax%2B1%2F2 through the points (-6,-4) and (-2,-1)


So from the graph we can see that the slope is 3%2F4 (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 4 units to get to the next point) the y-intercept is (0,0.5) ,or (0,1%2F2), and the x-intercept is (-0.666666666666667,0) ,or (-2%2F3,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=1%2F2 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,1%2F2).


So we have one point (0,1%2F2)






Now since the slope is 3%2F4, this means that in order to go from point to point we can use the slope to do so. So starting at (0,1%2F2), we can go up 3 units


and to the right 4 units to get to our next point



Now draw a line through those points to graph y=%283%2F4%29%2Ax%2B1%2F2


So this is the graph of y=%283%2F4%29%2Ax%2B1%2F2 through the points (0,0.5) and (4,3.5)



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


-2%2Ax-1%2Ay=-3Start with the given equation



-1%2Ay=-3%2B2%2Ax Add 2%2Ax to both sides

y=%28-1%29%28-3%2B2%2Ax%29 Multiply both sides by -1

y=%28-1%29%28-3%29%2B%281%29%28-2%29x%29 Distribute -1

y=3-%282%29x Multiply

y=-2%2Ax%2B3 Rearrange the terms

y=-2%2Ax%2B3 Reduce any fractions

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

So to graph this equation lets plug in some points

Plug in x=-3

y=-2%2A%28-3%29%2B3

y=6%2B3 Multiply

y=9 Add

So here's one point (-3,9)





Now lets find another point

Plug in x=-2

y=-2%2A%28-2%29%2B3

y=4%2B3 Multiply

y=7 Add

So here's another point (-2,7). Add this to our graph





Now draw a line through these points

So this is the graph of y=-2%2Ax%2B3 through the points (-3,9) and (-2,7)


So from the graph we can see that the slope is -2%2F1 (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 1 units to get to the next point), the y-intercept is (0,3)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=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 -2%2F1, 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 down 2 units


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



Now draw a line through those points to graph y=-2%2Ax%2B3


So this is the graph of y=-2%2Ax%2B3 through the points (0,3) and (1,1)