SOLUTION: I need help of the following equation: x + 3y = 4

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Question 83033: I need help of the following equation: x + 3y = 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


1%2Ax%2B3%2Ay=4Start with the given equation



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

y=%281%2F3%29%284-1%2Ax%29 Multiply both sides by 1%2F3

y=%281%2F3%29%284%29-%281%2F3%29%281%29x%29 Distribute 1%2F3

y=4%2F3-%281%2F3%29x Multiply

y=%28-1%2F3%29%2Ax%2B4%2F3 Rearrange the terms

y=%28-1%2F3%29%2Ax%2B4%2F3 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-1%2F3 (the slope) and b=4%2F3 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-8

y=%28-1%2F3%29%2A%28-8%29%2B4%2F3

y=8%2F3%2B4%2F3 Multiply

y=12%2F3 Add

y=4 Reduce

So here's one point (-8,4)





Now lets find another point

Plug in x=-5

y=%28-1%2F3%29%2A%28-5%29%2B4%2F3

y=5%2F3%2B4%2F3 Multiply

y=9%2F3 Add

y=3 Reduce

So here's another point (-5,3). Add this to our graph





Now draw a line through these points

So this is the graph of y=%28-1%2F3%29%2Ax%2B4%2F3 through the points (-8,4) and (-5,3)


So from the graph we can see that the slope is -1%2F3 (which tells us that in order to go from point to point we have to start at one point and go down -1 units and to the right 3 units to get to the next point), the y-intercept is (0,1.33333333333333) ,or (0,4%2F3), and the x-intercept is (4,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=4%2F3 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,4%2F3).


So we have one point (0,4%2F3)






Now since the slope is -1%2F3, this means that in order to go from point to point we can use the slope to do so. So starting at (0,4%2F3), we can go down 1 units


and to the right 3 units to get to our next point



Now draw a line through those points to graph y=%28-1%2F3%29%2Ax%2B4%2F3


So this is the graph of y=%28-1%2F3%29%2Ax%2B4%2F3 through the points (0,1.33333333333333) and (3,0.333333333333333)