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, we will create a table of values and plot the points on a graph.
For the first equation y(1) = 1/3x - 3:
x | y(1)
---------
3 | -2
6 | -1
-9 | -6
For the second equation y(2) = 1/3x + 1:
x | y(2)
---------
3 | 2
6 | 3
-9 | -2
Now, let's plot the points on a graph and connect them with a line:
Graph for the first equation:
(x,y) = (3, -2)
(x,y) = (6, -1)
(x,y) = (-9, -6)
Graph for the second equation:
(x,y) = (3, 2)
(x,y) = (6, 3)
(x,y) = (-9, -2)
The graph will have two lines, one representing each equation. The line for equation y(1) = 1/3x - 3 will have points (-9, -6), (3, -2), and (6, -1). The line for equation y(2) = 1/3x + 1 will have points (-9, -2), (3, 2), and (6, 3).
To graph the linear equations, we can create a table of values for x and calculate the corresponding y-values for each equation.
For y = (1/3)x - 3:
x | Y(1) = 1/3x - 3
------------------
3 | 1/3(3) - 3 = -2
6 | 1/3(6) - 3 = -1
-9 | 1/3(-9) - 3 = -6
For y = (1/3)x + 1:
x | Y(2) = 1/3x + 1
------------------
3 | 1/3(3) + 1 = 2
6 | 1/3(6) + 1 = 3
-9 | 1/3(-9) + 1 = -2
Now we can plot the points (x, y) for each equation on a graph:
(x, y) for y = (1/3)x - 3:
(3, -2)
(6, -1)
(-9, -6)
(x, y) for y = (1/3)x + 1:
(3, 2)
(6, 3)
(-9, -2)
Plotting these points on a graph, we get the lines for each equation.
To graph the linear equations, we need to substitute different x-values into the equations and calculate the corresponding y-values. Let's plug in the given x-values into the equations and fill out the table.
For y(1) = 1/3x - 3:
When x = 3:
y(1) = 1/3 * 3 - 3
y(1) = 1 - 3
y(1) = -2
When x = 6:
y(1) = 1/3 * 6 - 3
y(1) = 2 - 3
y(1) = -1
When x = -9:
y(1) = 1/3 * -9 - 3
y(1) = -3 - 3
y(1) = -6
Now let's calculate the values for y(2) = 1/3x + 1:
When x = 3:
y(2) = 1/3 * 3 + 1
y(2) = 1 + 1
y(2) = 2
When x = 6:
y(2) = 1/3 * 6 + 1
y(2) = 2 + 1
y(2) = 3
When x = -9:
y(2) = 1/3 * -9 + 1
y(2) = -3 + 1
y(2) = -2
Now, let's transfer the values to the table:
x | Y(1)1/3X-3 | Y(2)1/3X+1 | (X,Y)(1)) | (X,Y(2))
3 | -2 | 2 | (3,-2) | (3,2)
6 | -1 | 3 | (6,-1) | (6,3)
-9 | -6 | -2 | (-9,-6) | (-9,-2)
To graph the equations, plot the points (3,-2), (6,-1), and (-9,-6) for y(1) = 1/3x - 3, and plot the points (3,2), (6,3), and (-9,-2) for y(2) = 1/3x + 1. Then, connect the points with a straight line for each equation.