Question

Complete the table for the equation 3x−2y=6​, and graph the equation.

Answer 1

To complete the table, we need to choose values for x and solve for y.

Let's choose some values for x and find the corresponding values for y:

For x = 0:
3x - 2y = 6
3(0) - 2y = 6
0 - 2y = 6
-2y = 6
y = -3

So, one point on the graph is (0, -3).

For x = 2:
3x - 2y = 6
3(2) - 2y = 6
6 - 2y = 6
-2y = 0
y = 0

So, another point on the graph is (2, 0).

For x = 4:
3x - 2y = 6
3(4) - 2y = 6
12 - 2y = 6
-2y = -6
y = 3

So, another point on the graph is (4, 3).

Now, we can complete the table:

| x | y |
|---|---|
| 0 | -3 |
| 2 | 0 |
| 4 | 3 |

To graph the equation, we plot these points on a coordinate plane:

The graph should pass through the points (0, -3), (2, 0), and (4, 3).

The graph of the equation 3x - 2y = 6 is a straight line that passes through these points.