SOLUTION: 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 formula

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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


------------------------------------------------


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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