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Question 150559: I'm supposed to put the following formulas in y=mx+b form. Then I'm supposed to plot the Y intercept. Then to get the 2nd point I need to plot the rise and run of the two formulas. Last I need to give the point at which the two lines intersect. When I try these steps, it's not coming out right on my graph.
Plot the intersect points of the two equations
2x + y = 4
3x - 4y = 6
Answer in book is (2,0)
When I change the equations I get the following;
y = -2x/1 -4
y = 3/4x - 6/4 (I divided equation by -4 to get this solution)
Plot the intersect points of the two equations
x + 3y = -6
x - 3y = 0
Answer in book is (-3,-1)
When I change the equations I get the following;
y = -1/3x - 2 (I divided equation by 3 to get this solution)
y = 1/3x + 0 (I divided equation by -3 to get this solution)
Plot the intersect points of the two equations
3x - 2y = -6
-6x + 4y = 9
Answer in book is No solution
When I change the equations I get the following;
y = 3/2x + 3 (I divided equation by -2 to get this solution)
y = 3/2x + 9/4 (I divided equation by 4 to get this solution)
Plot the intersect points of the two equations
x + 2y = 4
-2x - 4y = -8
Answer in book is Infinite
When I change the equations I get the following;
y = -1/2x + 2 (I divided equation by 2 to get this solution)
y = 1/-2x + 2 (I divided equation by -4 to get this solution)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do the first one to get you started
First let's graph the equation 
Start with the first equation.
 Subtract  from both sides.
 Rearrange the terms.
Looking at we can see that the equation is in slope-intercept form  where the slope is  and the y-intercept is 
Since this tells us that the y-intercept is ) .Remember the y-intercept is the point where the graph intersects with the y-axis
So we have one point
Now since the slope is comprised of the "rise" over the "run" this means
Also, because the slope is  , this means:
which shows us that the rise is -2 and the run is 1. This means that to go from point to point, we can go down 2 and over 1
So starting at , go down 2 units
and to the right 1 unit to get to the next point )
Now draw a line through these points to graph
 So this is the graph of through the points and
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Now let's graph the equation 
Start with the second equation.
 Subtract  from both sides.
 Divide both sides by  to isolate  .
 Break up the fraction.
 Reduce
 Rearrange the terms.
Looking at we can see that the equation is in slope-intercept form where the slope is  and the y-intercept is 
Since this tells us that the y-intercept is ) .Remember the y-intercept is the point where the graph intersects with the y-axis
So we have one point
Now since the slope is comprised of the "rise" over the "run" this means
Also, because the slope is  , this means:
which shows us that the rise is 3 and the run is 4. This means that to go from point to point, we can go up 3 and over 4
So starting at , go up 3 units
and to the right 4 units to get to the next point )
Now draw a line through these points to graph
 So this is the graph of through the points and
======================================
So together the two graphs look like
 Graph of (red) and (green)
From the graph, we can see that the two lines intersect at the point (2,0). So the solution of the system is  and 
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