SOLUTION: I'm still having trouble with the graph method.Could someone please show me how to do a couple of my practice problems? Also when you draw the lines on the graph,could you please d

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Question 145290: I'm still having trouble with the graph method.Could someone please show me how to do a couple of my practice problems? Also when you draw the lines on the graph,could you please draw the dots first,so I can understand how you got where the lines go?
1) -x + y = -1
x + y = 3

2) 3x + y = -6
x + y = -4

I want to think you for all your help and time in advance.I think people like you are wonderful,because you help people like me that want to understand math concepts,but are still having some difficulties. Elle J
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
note: I added the solution to #2


# 1
Jump to problem #2
Once again, I'll do the first one to get you started (hopefully in the right direction)


Let's graph the first equation . To do this, we must first solve for y


Start with the first equation


Add to both sides


Rearrange the equation





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 1 and the run is 1. This means that to go from point to point, we can go up 1 and over 1



So starting at , go up 1 unit


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 second equation . To do this, we must first solve for y




Start with the second equation


Subtract from both sides


Rearrange the equation




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 -1 and the run is 1. This means that to go from point to point, we can go down 1 and over 1



So starting at , go down 1 unit


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 two equations together


Graph of (red) and (green)


So from the graph, we can see that the two lines intersect at the point (2,1).











# 2

Jump to problem #1

Let's graph the first equation . To do this, we must first solve for y



Start with the first equation


Subtract from both sides


Rearrange the equation




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 1. This means that to go from point to point, we can go down 3 and over 1



So starting at , go down 3 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


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


Let's graph the second equation . To do this, we must first solve for y


Start with the second equation


Subtract from both sides


Rearrange the equation





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 -1 and the run is 1. This means that to go from point to point, we can go down 1 and over 1



So starting at , go down 1 unit


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



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


Graph of (red) and (green)


So from the graph, we can see that the two lines intersect at the point (-1,-3).
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