Answer :
Let's break down the question into two parts:
a.) To create a table to graph the equation 3y = 6x - 12, we need to select values for x and solve for y using the equation. We will use the x-values provided: -10, -8, -6, -4, -2, 2, 4, 6, 8, and 10.
For each value of x, we plug it into the equation and solve for y:
To solve for y, we can simplify the equation first by dividing everything by 3:
3y = 6x - 12
y = 2x - 4
Now, we substitute each x value into this simplified equation to find y:
For x = -10:
y = 2 -10 - 4 = -20 - 4 = -24
For x = -8:
y = 2 -8 - 4 = -16 - 4 = -20
For x = -6:
y = 2 -6 - 4 = -12 - 4 = -16
For x = -4:
y = 2 -4 - 4 = -8 - 4 = -12
For x = -2:
y = 2 -2 - 4 = -4 - 4 = -8
For x = 2:
y = 2 2 - 4 = 4 - 4 = 0
For x = 4:
y = 2 4 - 4 = 8 - 4 = 4
For x = 6:
y = 2 6 - 4 = 12 - 4 = 8
For x = 8:
y = 2 8 - 4 = 16 - 4 = 12
For x = 10:
y = 2 10 - 4 = 20 - 4 = 16
Now, we create our table:
| x | y |
|------|------|
| -10 | -24 |
| -8 | -20 |
| -6 | -16 |
| -4 | -12 |
| -2 | -8 |
| 0 | -4 |
| 2 | 0 |
| 4 | 4 |
| 6 | 8 |
| 8 | 12 |
| 10 | 16 |
b.) To determine the intercepts of the graph, we look for the points where the line crosses the x-axis and the y-axis.
For the y-intercept, we set x to 0 in our simplified equation y = 2x - 4:
y = 2(0) - 4 = -4
Thus, the y-intercept is (0, -4).
For the x-intercept, we set y to 0 in the same equation and solve for x:
0 = 2x - 4
4 = 2x
x = 4/2
x = 2
Therefore, the x-intercept is (2, 0).
So the intercepts of the graph are:
x-intercept: (2, 0)
y-intercept: (0, -4)
a.) To create a table to graph the equation 3y = 6x - 12, we need to select values for x and solve for y using the equation. We will use the x-values provided: -10, -8, -6, -4, -2, 2, 4, 6, 8, and 10.
For each value of x, we plug it into the equation and solve for y:
To solve for y, we can simplify the equation first by dividing everything by 3:
3y = 6x - 12
y = 2x - 4
Now, we substitute each x value into this simplified equation to find y:
For x = -10:
y = 2 -10 - 4 = -20 - 4 = -24
For x = -8:
y = 2 -8 - 4 = -16 - 4 = -20
For x = -6:
y = 2 -6 - 4 = -12 - 4 = -16
For x = -4:
y = 2 -4 - 4 = -8 - 4 = -12
For x = -2:
y = 2 -2 - 4 = -4 - 4 = -8
For x = 2:
y = 2 2 - 4 = 4 - 4 = 0
For x = 4:
y = 2 4 - 4 = 8 - 4 = 4
For x = 6:
y = 2 6 - 4 = 12 - 4 = 8
For x = 8:
y = 2 8 - 4 = 16 - 4 = 12
For x = 10:
y = 2 10 - 4 = 20 - 4 = 16
Now, we create our table:
| x | y |
|------|------|
| -10 | -24 |
| -8 | -20 |
| -6 | -16 |
| -4 | -12 |
| -2 | -8 |
| 0 | -4 |
| 2 | 0 |
| 4 | 4 |
| 6 | 8 |
| 8 | 12 |
| 10 | 16 |
b.) To determine the intercepts of the graph, we look for the points where the line crosses the x-axis and the y-axis.
For the y-intercept, we set x to 0 in our simplified equation y = 2x - 4:
y = 2(0) - 4 = -4
Thus, the y-intercept is (0, -4).
For the x-intercept, we set y to 0 in the same equation and solve for x:
0 = 2x - 4
4 = 2x
x = 4/2
x = 2
Therefore, the x-intercept is (2, 0).
So the intercepts of the graph are:
x-intercept: (2, 0)
y-intercept: (0, -4)
