SOLUTION: 3x+2y=8

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Question 125469This question is from textbook Structure and Method Book 1
: 3x+2y=8 This question is from textbook Structure and Method Book 1

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Graphing Linear Equations


3%2Ax%2B2%2Ay=8Start with the given equation



2%2Ay=8-3%2Ax Subtract 3%2Ax from both sides

y=%281%2F2%29%288-3%2Ax%29 Multiply both sides by 1%2F2

y=%281%2F2%29%288%29-%281%2F2%29%283%29x%29 Distribute 1%2F2

y=8%2F2-%283%2F2%29x Multiply

y=%28-3%2F2%29%2Ax%2B8%2F2 Rearrange the terms

y=%28-3%2F2%29%2Ax%2B4 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-3%2F2 (the slope) and b=4 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-2

y=%28-3%2F2%29%2A%28-2%29%2B4

y=6%2F2%2B4 Multiply

y=14%2F2 Add

y=7 Reduce

So here's one point (-2,7)





Now lets find another point

Plug in x=0

y=%28-3%2F2%29%2A%280%29%2B4

y=0%2F2%2B4 Multiply

y=8%2F2 Add

y=4 Reduce

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=%28-3%2F2%29%2Ax%2B4 through the points (-2,7) and (0,4)


So from the graph we can see that the slope is -3%2F2 (which tells us that in order to go from point to point we have to start at one point and go down -3 units and to the right 2 units to get to the next point), the y-intercept is (0,4)and the x-intercept is (2.66666666666667,0) ,or (8%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%2F2, 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 down 3 units


and to the right 2 units to get to our next point



Now draw a line through those points to graph y=%28-3%2F2%29%2Ax%2B4


So this is the graph of y=%28-3%2F2%29%2Ax%2B4 through the points (0,4) and (2,1)