Question

Which graph matches the linear equation: −2x+3y=−6
(1 point)
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Answer 1

To match a graph with the linear equation \(-2x + 3y = -6\), we first need to rearrange it into slope-intercept form (y = mx + b), which will make it easier to identify the line's characteristics such as slope and y-intercept.

Starting with the equation:
\[
-2x + 3y = -6
\]
we can solve for \(y\):

1. Add \(2x\) to both sides:
\[
3y = 2x - 6
\]

2. Divide every term by \(3\):
\[
y = \frac{2}{3}x - 2
\]

Now, we have the equation in slope-intercept form \(y = \frac{2}{3}x - 2\).

From this, we can identify:
- The slope \(m\) is \(\frac{2}{3}\).
- The y-intercept is \(-2\).

This means the line crosses the y-axis at the point \((0, -2)\) and rises 2 units for every 3 units it moves to the right.

To match the graph:
- Look for a line that crosses the y-axis at \(-2\).
- The line should have a positive slope, indicating it rises from left to right.

If you have specific graph options, you can apply this information to determine which graph corresponds to the equation \(-2x + 3y = -6\).