SOLUTION: how would you solve and graph 2x+y=1

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Question 614162: how would you solve and graph 2x+y=1
Answer by radh(108) About Me  (Show Source):
You can put this solution on YOUR website!
Let's convert this into slope-form. Slope-intercept form is: y=mx%2Bb. So, switch the sides of the y and the 1 to get: 2x-1=-y. Change the negative y to a positive y by flipping the signs of everything on the other side: -2x%2B1=y would be your final form.

Now, we can graph using a solver.

Solved by pluggable solver: Graphing Linear Equations
In order to graph y=-2%2Ax%2B1 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-4

y=-2%2A%28-4%29%2B1

y=8%2B1 Multiply

y=9 Add

So here's one point (-4,9)




Now lets find another point

Plug in x=-3

y=-2%2A%28-3%29%2B1

y=6%2B1 Multiply

y=7 Add

So here's another point (-3,7). Add this to our graph





Now draw a line through these points

So this is the graph of y=-2%2Ax%2B1 through the points (-4,9) and (-3,7)


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 (0,1)and the x-intercept is (0.5,0) ,or (1%2F2,0)


We could graph this equation another way. Since b=1 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,1).


So we have one point (0,1)





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 (0,1), 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%2B1


So this is the graph of y=-2%2Ax%2B1 through the points (0,1) and (1,-1)