SOLUTION: 2x-y=5

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Question 125467This question is from textbook Structure and Method Book 1
: 2x-y=5 This question is from textbook Structure and Method Book 1

Answer by MathLover1(20849) About Me  (Show Source):
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Solved by pluggable solver: Graphing Linear Equations


2%2Ax-1%2Ay=5Start with the given equation



-1%2Ay=5-2%2Ax Subtract 2%2Ax from both sides

y=%28-1%29%285-2%2Ax%29 Multiply both sides by -1

y=%28-1%29%285%29%2B%281%29%282%29x%29 Distribute -1

y=-5%2B%282%29x Multiply

y=2%2Ax-5 Rearrange the terms

y=2%2Ax-5 Reduce any fractions

So the equation is now in slope-intercept form (y=mx%2Bb) where m=2 (the slope) and b=-5 (the y-intercept)

So to graph this equation lets plug in some points

Plug in x=-2

y=2%2A%28-2%29-5

y=-4-5 Multiply

y=-9 Add

So here's one point (-2,-9)





Now lets find another point

Plug in x=-1

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

y=-2-5 Multiply

y=-7 Add

So here's another point (-1,-7). Add this to our graph





Now draw a line through these points

So this is the graph of y=2%2Ax-5 through the points (-2,-9) and (-1,-7)


So from the graph we can see that the slope is 2%2F1 (which tells us that in order to go from point to point we have to start at one point and go up 2 units and to the right 1 units to get to the next point) the y-intercept is (0,-5)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=-5 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-5).


So we have one point (0,-5)






Now since the slope is 2%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-5), we can go up 2 units


and to the right 1 units to get to our next point



Now draw a line through those points to graph y=2%2Ax-5


So this is the graph of y=2%2Ax-5 through the points (0,-5) and (1,-3)