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

Algebra ->  Graphs -> 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      Log On


   

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) About Me  (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 -x+%2B+y+=+-1. To do this, we must first solve for y


-x%2By=-1 Start with the first equation


y=-1%2Bx Add +x to both sides


y=x-1 Rearrange the equation





Looking at y=x-1 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=1 and the y-intercept is b=-1


Since b=-1 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
slope=rise%2Frun

Also, because the slope is 1, this means:

rise%2Frun=1%2F1


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 y=x-1

So this is the graph of y=x-1 through the points and



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



Now let's graph the second equation x+%2B+y+=+3. To do this, we must first solve for y




x%2By=3 Start with the second equation


y=3-x Subtract +x from both sides


y=-x%2B3 Rearrange the equation




Looking at y=-x%2B3 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-1 and the y-intercept is b=3


Since b=3 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
slope=rise%2Frun

Also, because the slope is -1, this means:

rise%2Frun=-1%2F1


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 y=-x%2B3

So this is the graph of y=-x%2B3 through the points and


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


Now let's graph the two equations together


Graph of y=x-1 (red) and y=-x%2B3 (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 3x+%2B+y+=+-6. To do this, we must first solve for y



3x%2By=-6 Start with the first equation


y=-6-3x Subtract 3+x from both sides


y=-3x-6 Rearrange the equation




Looking at y=-3x-6 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-3 and the y-intercept is b=-6


Since b=-6 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
slope=rise%2Frun

Also, because the slope is -3, this means:

rise%2Frun=-3%2F1


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 y=-3x-6

So this is the graph of y=-3x-6 through the points and


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


Let's graph the second equation x+%2B+y+=+-4+. To do this, we must first solve for y


x%2By=-4 Start with the second equation


y=-4-x Subtract +x from both sides


y=-x-4 Rearrange the equation





Looking at y=-x-4 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-1 and the y-intercept is b=-4


Since b=-4 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
slope=rise%2Frun

Also, because the slope is -1, this means:

rise%2Frun=-1%2F1


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 y=-x-4

So this is the graph of y=-x-4 through the points and



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


Graph of y=-3x-6 (red) and y=-x-4 (green)


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