Graph the linear equations using a table of values.
y(1) =1/3x - 3
y(2) = 1/3x + 1
x
y(1)
1/3x-3
y(2)
1/3x + 1
(x,y(1))
(x, y(2))
3
6
-9
To graph the linear equations using a table of values, we can substitute different values of x into the equations and calculate the corresponding y values.
For y(1) = 1/3x - 3:
x | y(1)
--------
-3 | -4
0 | -3
3 | -2
For y(2) = 1/3x + 1:
x | y(2)
--------
-3 | 0
0 | 1
3 | 2
Using these values, we can plot the points on a graph and draw a line through them.
For y(1):
(-3, -4)
(0, -3)
(3, -2)
For y(2):
(-3, 0)
(0, 1)
(3, 2)
Now we can connect the points with a straight line:
what about the 3rd column?
Apologies for the confusion. It seems there was a misunderstanding regarding the 3rd column. Let's correct it.
To find the values of y(1) and y(2) given x, we can substitute the x-values into the equations.
For y(1) = 1/3x - 3:
x | y(1)
--------
1 | -2
2 | -1
3 | 0
For y(2) = 1/3x + 1:
x | y(2)
--------
1 | 1.33
2 | 1.67
3 | 2
Using these values, we can plot the points on a graph and draw a line through them.
For y(1):
(1, -2)
(2, -1)
(3, 0)
For y(2):
(1, 1.33)
(2, 1.67)
(3, 2)
Now we can connect the points with a straight line:
no column (x,y(1))
(x, y(2))
its together
I apologize for the confusion. Here's the corrected version:
To graph the linear equations using a table of values:
For y(1) = 1/3x - 3:
x | y(1) = 1/3x - 3
-------------------
-3 | -4
0 | -3
3 | -2
For y(2) = 1/3x + 1:
x | y(2) = 1/3x + 1
-------------------
-3 | 0
0 | 1
3 | 2
Plotting the points on a graph and connecting them:
For y(1):
(-3, -4)
(0, -3)
(3, -2)
For y(2):
(-3, 0)
(0, 1)
(3, 2)
Now, let's plot these points on a graph:
Here is the graph:
|
3 ----|-------------------------
|
|
2 ----|-------•
| /
|
1 ----|--•
| /
|
0 ----|-------------------------
|
|
-3 ----|--•---------------------
| /
|
-4 ----|-------------------------
|
-3 0 3 6 9
The line connecting the points represents each linear equation. The first equation y(1) = 1/3x - 3 is represented by a line that passes through (-3, -4), (0, -3), and (3, -2). The second equation y(2) = 1/3x + 1 is represented by a line that passes through (-3, 0), (0, 1), and (3, 2).
Graph the linear equations using a table of values.
y(1) =1/3x - 3
y(2) = 1/3x + 1
x
y(1)
1/3x-3
y(2)
1/3x + 1
(x,y(1))
(x, y(2))
3
-4
0
6
-3
1
-9
-2
2
To graph the linear equations using the given table of values:
For y(1) = 1/3x - 3:
x | y(1) = 1/3x - 3
----------------------
3 | -4
6 | -3
-9 | -2
For y(2) = 1/3x + 1:
x | y(2) = 1/3x + 1
---------------------
3 | 0
6 | 1
-9 | 2
Now, let's plot these points on a graph:
For y(1):
(3, -4)
(6, -3)
(-9, -2)
For y(2):
(3, 0)
(6, 1)
(-9, 2)
Here is the graph:
|
3 ----|-------------------------
|
|
2 ----|-------•
| /
|
1 ----|--•
| /
|
0 ----|-------------------------
|
|
-1 ----|--•---------------------
| /
|
-2 ----|-------------------------
|
-9 -6 -3 0 3 6
The line connecting the points represents each linear equation. The first equation, y(1) = 1/3x - 3, is represented by a line that passes through (3, -4), (6, -3), and (-9, -2). The second equation, y(2) = 1/3x + 1, is represented by a line that passes through (3, 0), (6, 1), and (-9, 2).