SOLUTION: Graph 3x-y=4

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Question 110723: Graph 3x-y=4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Graphing Linear Equations


3%2Ax-1%2Ay=4Start with the given equation



-1%2Ay=4-3%2Ax Subtract 3%2Ax from both sides

y=%28-1%29%284-3%2Ax%29 Multiply both sides by -1

y=%28-1%29%284%29%2B%281%29%283%29x%29 Distribute -1

y=-4%2B%283%29x Multiply

y=3%2Ax-4 Rearrange the terms

y=3%2Ax-4 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=3 (the slope) and b=-4 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-1

y=3%2A%28-1%29-4

y=-3-4 Multiply

y=-7 Add

So here's one point (-1,-7)





Now lets find another point

Plug in x=0

y=3%2A%280%29-4

y=0-4 Multiply

y=-4 Add

So here's another point (0,-4). Add this to our graph





Now draw a line through these points

So this is the graph of y=3%2Ax-4 through the points (-1,-7) and (0,-4)


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,-4)and the x-intercept is (1.33333333333333,0) ,or (4%2F3,0) . 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 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,-4), 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-4


So this is the graph of y=3%2Ax-4 through the points (0,-4) and (1,-1)