SOLUTION: Graph the following lines, you may use whichever method. 1. y=x-2 2. y=-2x+5 3. y=-x-2 4. y=5/3x-4 5. y=2x 6. y=-1/2x+3

Algebra ->  Graphs -> SOLUTION: Graph the following lines, you may use whichever method. 1. y=x-2 2. y=-2x+5 3. y=-x-2 4. y=5/3x-4 5. y=2x 6. y=-1/2x+3      Log On


   

Question 922877: Graph the following lines, you may use whichever method.
1. y=x-2
2. y=-2x+5
3. y=-x-2
4. y=5/3x-4
5. y=2x
6. y=-1/2x+3
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1.+y=x-2
Solved by pluggable solver: Graphing Linear Equations
In order to graph y=1%2Ax-2 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-7

y=1%2A%28-7%29-2

y=-7-2 Multiply

y=-9 Add

So here's one point (-7,-9)




Now lets find another point

Plug in x=-6

y=1%2A%28-6%29-2

y=-6-2 Multiply

y=-8 Add

So here's another point (-6,-8). Add this to our graph





Now draw a line through these points

So this is the graph of y=1%2Ax-2 through the points (-7,-9) and (-6,-8)


So from the graph we can see that the slope is 1%2F1 (which tells us that in order to go from point to point we have to start at one point and go up 1 units and to the right 1 units to get to the next point) the y-intercept is (0,-2)and the x-intercept is (2,0)


We could graph this equation another way. Since b=-2 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-2).


So we have one point (0,-2)





Now since the slope is 1%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-2), we can go up 1 units



and to the right 1 units to get to our next point


Now draw a line through those points to graph y=1%2Ax-2


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



2. y=-2x%2B5
Solved by pluggable solver: Graphing Linear Equations
In order to graph y=-2%2Ax%2B5 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-2

y=-2%2A%28-2%29%2B5

y=4%2B5 Multiply

y=9 Add

So here's one point (-2,9)




Now lets find another point

Plug in x=-1

y=-2%2A%28-1%29%2B5

y=2%2B5 Multiply

y=7 Add

So here's another point (-1,7). Add this to our graph





Now draw a line through these points

So this is the graph of y=-2%2Ax%2B5 through the points (-2,9) and (-1,7)


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 (0,5)and the x-intercept is (2.5,0) ,or (5%2F2,0)


We could graph this equation another way. Since b=5 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,5).


So we have one point (0,5)





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 (0,5), 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%2B5


So this is the graph of y=-2%2Ax%2B5 through the points (0,5) and (1,3)



3. y=-x-2
Solved by pluggable solver: Graphing Linear Equations
In order to graph y=-1%2Ax-2 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-9

y=-1%2A%28-9%29-2

y=9-2 Multiply

y=7 Add

So here's one point (-9,7)




Now lets find another point

Plug in x=-8

y=-1%2A%28-8%29-2

y=8-2 Multiply

y=6 Add

So here's another point (-8,6). Add this to our graph





Now draw a line through these points

So this is the graph of y=-1%2Ax-2 through the points (-9,7) and (-8,6)


So from the graph we can see that the slope is -1%2F1 (which tells us that in order to go from point to point we have to start at one point and go down -1 units and to the right 1 units to get to the next point), the y-intercept is (0,-2)and the x-intercept is (-2,0)


We could graph this equation another way. Since b=-2 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-2).


So we have one point (0,-2)





Now since the slope is -1%2F1, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-2), we can go down 1 units



and to the right 1 units to get to our next point


Now draw a line through those points to graph y=-1%2Ax-2


So this is the graph of y=-1%2Ax-2 through the points (0,-2) and (1,-3)


4. y=%285%2F3%29x-4
Solved by pluggable solver: Graphing Linear Equations
In order to graph y=%285%2F3%29%2Ax-4 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-3

y=%285%2F3%29%2A%28-3%29-4

y=-15%2F3-4 Multiply

y=-27%2F3 Add

y=-9 Reduce

So here's one point (-3,-9)




Now lets find another point

Plug in x=0

y=%285%2F3%29%2A%280%29-4

y=0%2F3-4 Multiply

y=-12%2F3 Add

y=-4 Reduce

So here's another point (0,-4). Add this to our graph





Now draw a line through these points

So this is the graph of y=%285%2F3%29%2Ax-4 through the points (-3,-9) and (0,-4)


So from the graph we can see that the slope is 5%2F3 (which tells us that in order to go from point to point we have to start at one point and go up 5 units and to the right 3 units to get to the next point) the y-intercept is (0,-4)and the x-intercept is (2.4,0) ,or (12%2F5,0)


We could graph this equation another way. Since b=-4 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,-4).


So we have one point (0,-4)





Now since the slope is 5%2F3, this means that in order to go from point to point we can use the slope to do so. So starting at (0,-4), we can go up 5 units



and to the right 3 units to get to our next point


Now draw a line through those points to graph y=%285%2F3%29%2Ax-4


So this is the graph of y=%285%2F3%29%2Ax-4 through the points (0,-4) and (3,1)



5. y=2x
Solved by pluggable solver: Graphing Linear Equations
In order to graph y=2%2Ax%2B0 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%2B0

y=-8%2B0 Multiply

y=-8 Add

So here's one point (-4,-8)




Now lets find another point

Plug in x=-3

y=2%2A%28-3%29%2B0

y=-6%2B0 Multiply

y=-6 Add

So here's another point (-3,-6). Add this to our graph





Now draw a line through these points

So this is the graph of y=2%2Ax%2B0 through the points (-4,-8) and (-3,-6)


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 up 2 units and to the right 1 units to get to the next point) the y-intercept is (0,0)and the x-intercept is (0,0)


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


So we have one point (0,0)





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 (0,0), we can go up 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%2B0


So this is the graph of y=2%2Ax%2B0 through the points (0,0) and (1,2)



6. y=-%281%2F2%29x%2B3
Solved by pluggable solver: Graphing Linear Equations
In order to graph y=%28-1%2F2%29%2Ax%2B3 we only need to plug in two points to draw the line

So lets plug in some points

Plug in x=-8

y=%28-1%2F2%29%2A%28-8%29%2B3

y=8%2F2%2B3 Multiply

y=14%2F2 Add

y=7 Reduce

So here's one point (-8,7)




Now lets find another point

Plug in x=-6

y=%28-1%2F2%29%2A%28-6%29%2B3

y=6%2F2%2B3 Multiply

y=12%2F2 Add

y=6 Reduce

So here's another point (-6,6). Add this to our graph





Now draw a line through these points

So this is the graph of y=%28-1%2F2%29%2Ax%2B3 through the points (-8,7) and (-6,6)


So from the graph we can see that the slope is -1%2F2 (which tells us that in order to go from point to point we have to start at one point and go down -1 units and to the right 2 units to get to the next point), the y-intercept is (0,3)and the x-intercept is (6,0)


We could graph this equation another way. Since b=3 this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,3).


So we have one point (0,3)





Now since the slope is -1%2F2, this means that in order to go from point to point we can use the slope to do so. So starting at (0,3), we can go down 1 units



and to the right 2 units to get to our next point


Now draw a line through those points to graph y=%28-1%2F2%29%2Ax%2B3


So this is the graph of y=%28-1%2F2%29%2Ax%2B3 through the points (0,3) and (2,2)