SOLUTION: Solve each of the following by graphing 3x-y=3 3x-y=6

Algebra ->  Systems-of-equations -> SOLUTION: Solve each of the following by graphing 3x-y=3 3x-y=6      Log On


   

Question 107770: Solve each of the following by graphing
3x-y=3
3x-y=6
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

3x-y=3
here is the graph:

Solved by pluggable solver: Graphing Linear Equations


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



-1%2Ay=3-3%2Ax Subtract 3%2Ax from both sides

y=%28-1%29%283-3%2Ax%29 Multiply both sides by -1

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

y=-3%2B%283%29x Multiply

y=3%2Ax-3 Rearrange the terms

y=3%2Ax-3 Reduce any fractions

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

So to graph this equation lets plug in some points

Plug in x=-2

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

y=-6-3 Multiply

y=-9 Add

So here's one point (-2,-9)





Now lets find another point

Plug in x=-1

y=3%2A%28-1%29-3

y=-3-3 Multiply

y=-6 Add

So here's another point (-1,-6). Add this to our graph





Now draw a line through these points

So this is the graph of y=3%2Ax-3 through the points (-2,-9) and (-1,-6)


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


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



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


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



3x-y=6

here is the graph:


Solved by pluggable solver: Graphing Linear Equations


3%2Ax-1%2Ay=6Start with the given equation



-1%2Ay=6-3%2Ax Subtract 3%2Ax from both sides

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

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

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

y=3%2Ax-6 Rearrange the terms

y=3%2Ax-6 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=3 (the slope) and b=-6 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-1

y=3%2A%28-1%29-6

y=-3-6 Multiply

y=-9 Add

So here's one point (-1,-9)





Now lets find another point

Plug in x=0

y=3%2A%280%29-6

y=0-6 Multiply

y=-6 Add

So here's another point (0,-6). Add this to our graph





Now draw a line through these points

So this is the graph of y=3%2Ax-6 through the points (-1,-9) and (0,-6)


So from the graph we can see that the slope is 3%2F1 (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 1 units to get to the next point) the y-intercept is (0,-6)and the x-intercept is (2,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=-6 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-6).


So we have one point (0,-6)






Now since the slope is 3%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-6), we can go up 3 units


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



Now draw a line through those points to graph y=3%2Ax-6


So this is the graph of y=3%2Ax-6 through the points (0,-6) and (1,-3)