Question

Graph this equation
2x–3y=–6

Answer 1

To graph the equation \(2x - 3y = -6\), we can rearrange it into slope-intercept form (\(y = mx + b\)).

1. Start with the original equation:

\[
2x - 3y = -6
\]

2. Solve for \(y\):

\[
-3y = -2x - 6
\]
\[
y = \frac{2}{3}x + 2
\]

Now, we can identify the slope (\(m\)) and the y-intercept (\(b\)):
- The slope \(m = \frac{2}{3}\)
- The y-intercept \(b = 2\) (the point where the line crosses the y-axis)

3. To graph the line:
- Start at the y-intercept (0, 2) on the graph.
- From that point, use the slope to find another point. Since the slope is \(\frac{2}{3}\), go up 2 units and to the right 3 units. This brings you to the point (3, 4).
- You can also find a third point by going in the opposite direction: from (0, 2), go down 2 units and to the left 3 units, which brings you to the point (-3, 0).

4. Plot the points (0, 2), (3, 4), and (-3, 0) on a coordinate plane.

5. Draw a straight line through the points.

This will give you the graph of the equation \(2x - 3y = -6\).