SOLUTION: Hello, my name is Allison and I need help graphing (and solving) this equation: 3x-4y=24 I've tried subtracting 4y from each side of the equation, but that just got me confused.

Algebra ->  Absolute-value -> SOLUTION: Hello, my name is Allison and I need help graphing (and solving) this equation: 3x-4y=24 I've tried subtracting 4y from each side of the equation, but that just got me confused.      Log On


   

Question 399069: Hello, my name is Allison and I need help graphing (and solving) this equation: 3x-4y=24
I've tried subtracting 4y from each side of the equation, but that just got me confused.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Hello Allison, here is a solution!

3x-4y=24

Solved by pluggable solver: Graphing Linear Equations


3%2Ax-4%2Ay=24Start with the given equation



-4%2Ay=24-3%2Ax Subtract 3%2Ax from both sides

y=%28-1%2F4%29%2824-3%2Ax%29 Multiply both sides by -1%2F4

y=%28-1%2F4%29%2824%29%2B%281%2F4%29%283%29x%29 Distribute -1%2F4

y=-24%2F4%2B%283%2F4%29x Multiply

y=%283%2F4%29%2Ax-24%2F4 Rearrange the terms

y=%283%2F4%29%2Ax-6 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=3%2F4 (the slope) and b=-6 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-4

y=%283%2F4%29%2A%28-4%29-6

y=-12%2F4-6 Multiply

y=-36%2F4 Add

y=-9 Reduce

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





Now lets find another point

Plug in x=0

y=%283%2F4%29%2A%280%29-6

y=0%2F4-6 Multiply

y=-24%2F4 Add

y=-6 Reduce

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=%283%2F4%29%2Ax-6 through the points (-4,-9) and (0,-6)


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,-6)and the x-intercept is (8,0) . 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%2F4, 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 4 units to get to our next point



Now draw a line through those points to graph y=%283%2F4%29%2Ax-6


So this is the graph of y=%283%2F4%29%2Ax-6 through the points (0,-6) and (4,-3)