To find the graph that matches the linear equation \(-2x + 3y = -6\), we can first rewrite the equation in slope-intercept form \(y = mx + b\) where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the equation:
\[ -2x + 3y = -6 \]
We can isolate \(y\):
- Add \(2x\) to both sides:
\[ 3y = 2x - 6 \]
- Divide everything by 3:
\[ y = \frac{2}{3}x - 2 \]
From this, we see that the slope \(m\) is \(\frac{2}{3}\) and the y-intercept \(b\) is \(-2\).
This means that the graph will have the following characteristics:
- It crosses the y-axis at the point (0, -2).
- It rises \(\frac{2}{3}\) units for every 1 unit it moves to the right.
When looking for the correct graph, check for these features to find the one that matches \(y = \frac{2}{3}x - 2\). If you have multiple response options, look for a graph with these properties.