SOLUTION: determine the x-intercept of the graph: 2x+4y+=8

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Question 396690: determine the x-intercept of the graph: 2x+4y+=8
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Graphing Linear Equations


2%2Ax%2B4%2Ay=8Start with the given equation



4%2Ay=8-2%2Ax Subtract 2%2Ax from both sides

y=%281%2F4%29%288-2%2Ax%29 Multiply both sides by 1%2F4

y=%281%2F4%29%288%29-%281%2F4%29%282%29x%29 Distribute 1%2F4

y=8%2F4-%282%2F4%29x Multiply

y=%28-2%2F4%29%2Ax%2B8%2F4 Rearrange the terms

y=%28-1%2F2%29%2Ax%2B2 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=-1%2F2 (the slope) and b=2 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-8

y=%28-1%2F2%29%2A%28-8%29%2B2

y=8%2F2%2B2 Multiply

y=12%2F2 Add

y=6 Reduce

So here's one point (-8,6)





Now lets find another point

Plug in x=-6

y=%28-1%2F2%29%2A%28-6%29%2B2

y=6%2F2%2B2 Multiply

y=10%2F2 Add

y=5 Reduce

So here's another point (-6,5). Add this to our graph





Now draw a line through these points

So this is the graph of y=%28-1%2F2%29%2Ax%2B2 through the points (-8,6) and (-6,5)


So from the graph we can see that the slope is -1%2F2 (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 2 units to get to the next point), the y-intercept is (0,2)and the x-intercept is (4,0) . 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 -1%2F2, 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 1 units


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



Now draw a line through those points to graph y=%28-1%2F2%29%2Ax%2B2


So this is the graph of y=%28-1%2F2%29%2Ax%2B2 through the points (0,2) and (2,1)



as you can see from the graph, x-intercept is in (4,0)