SOLUTION: How would you graph 3x-7y=14

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Question 122031: How would you graph 3x-7y=14
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Graphing Linear Equations


3%2Ax-7%2Ay=14Start with the given equation



-7%2Ay=14-3%2Ax Subtract 3%2Ax from both sides

y=%28-1%2F7%29%2814-3%2Ax%29 Multiply both sides by -1%2F7

y=%28-1%2F7%29%2814%29%2B%281%2F7%29%283%29x%29 Distribute -1%2F7

y=-14%2F7%2B%283%2F7%29x Multiply

y=%283%2F7%29%2Ax-14%2F7 Rearrange the terms

y=%283%2F7%29%2Ax-2 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=3%2F7 (the slope) and b=-2 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-7

y=%283%2F7%29%2A%28-7%29-2

y=-21%2F7-2 Multiply

y=-35%2F7 Add

y=-5 Reduce

So here's one point (-7,-5)





Now lets find another point

Plug in x=0

y=%283%2F7%29%2A%280%29-2

y=0%2F7-2 Multiply

y=-14%2F7 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=%283%2F7%29%2Ax-2 through the points (-7,-5) and (0,-2)


So from the graph we can see that the slope is 3%2F7 (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 7 units to get to the next point) the y-intercept is (0,-2)and the x-intercept is (4.66666666666667,0) ,or (14%2F3,0) . 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 3%2F7, 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 3 units


and to the right 7 units to get to our next point



Now draw a line through those points to graph y=%283%2F7%29%2Ax-2


So this is the graph of y=%283%2F7%29%2Ax-2 through the points (0,-2) and (7,1)