SOLUTION: graph: 4x+5y=10

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Question 414162: graph: 4x+5y=10
Answer by MathLover1(20849) About Me  (Show Source):
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4x%2B5y=10
graph:
Solved by pluggable solver: Graphing Linear Equations


4%2Ax%2B5%2Ay=10Start with the given equation



5%2Ay=10-4%2Ax Subtract 4%2Ax from both sides

y=%281%2F5%29%2810-4%2Ax%29 Multiply both sides by 1%2F5

y=%281%2F5%29%2810%29-%281%2F5%29%284%29x%29 Distribute 1%2F5

y=10%2F5-%284%2F5%29x Multiply

y=%28-4%2F5%29%2Ax%2B10%2F5 Rearrange the terms

y=%28-4%2F5%29%2Ax%2B2 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-4%2F5 (the slope) and b=2 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-5

y=%28-4%2F5%29%2A%28-5%29%2B2

y=20%2F5%2B2 Multiply

y=30%2F5 Add

y=6 Reduce

So here's one point (-5,6)





Now lets find another point

Plug in x=0

y=%28-4%2F5%29%2A%280%29%2B2

y=0%2F5%2B2 Multiply

y=10%2F5 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=%28-4%2F5%29%2Ax%2B2 through the points (-5,6) and (0,2)


So from the graph we can see that the slope is -4%2F5 (which tells us that in order to go from point to point we have to start at one point and go down -4 units and to the right 5 units to get to the next point), the y-intercept is (0,2)and the x-intercept is (2.5,0) ,or (5%2F2,0) . 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 -4%2F5, 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 down 4 units


and to the right 5 units to get to our next point



Now draw a line through those points to graph y=%28-4%2F5%29%2Ax%2B2


So this is the graph of y=%28-4%2F5%29%2Ax%2B2 through the points (0,2) and (5,-2)