SOLUTION: 2x + y = 3 with no given numbers

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Question 119657: 2x + y = 3 with no given numbers
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to graph?

Solved by pluggable solver: Graphing Linear Equations


2%2Ax%2B1%2Ay=3Start with the given equation



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

y=%281%29%283-2%2Ax%29 Multiply both sides by 1

y=%281%29%283%29-%281%29%282%29x%29 Distribute 1

y=3-%282%29x Multiply

y=-2%2Ax%2B3 Rearrange the terms

y=-2%2Ax%2B3 Reduce any fractions

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

So to graph this equation lets plug in some points

Plug in x=-3

y=-2%2A%28-3%29%2B3

y=6%2B3 Multiply

y=9 Add

So here's one point (-3,9)





Now lets find another point

Plug in x=-2

y=-2%2A%28-2%29%2B3

y=4%2B3 Multiply

y=7 Add

So here's another point (-2,7). Add this to our graph





Now draw a line through these points

So this is the graph of y=-2%2Ax%2B3 through the points (-3,9) and (-2,7)


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 down -2 units and to the right 1 units to get to the next point), the y-intercept is (0,3)and the x-intercept is (1.5,0) ,or (3%2F2,0) . So all of this information verifies our graph.


We could graph this equation another way. Since b=3 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,3).


So we have one point (0,3)






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 (0,3), we can go down 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%2B3


So this is the graph of y=-2%2Ax%2B3 through the points (0,3) and (1,1)