Which of the following statements is true about the graph of the equation 2y − 3x = −4 in the xy-plane?

Options

A. It has a negative slope and a positive y-intercept.
B. It has a negative slope and a negative y-intercept.
C. It has a positive slope and a positive y-intercept.
D. It has a positive slope and a negative y-intercept.

Explanation

To determine which statement is true about the graph of the equation \(2y - 3x = -4\) in the xy-plane, we will convert the equation into the slope-intercept form \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.

### Step 1: Rewrite the equation
Start with the given equation:
\[ 2y - 3x = -4 \]

### Step 2: Isolate \(y\)
Add \(3x\) to both sides:
\[ 2y = 3x - 4 \]

### Step 3: Divide by 2
Now, divide every term by 2 to solve for \(y\):
\[ y = \frac{3}{2}x - 2 \]

### Step 4: Identify the slope and y-intercept
From the equation \(y = \frac{3}{2}x - 2\):
- The slope \(m\) is \(\frac{3}{2}\) (which is positive).
- The y-intercept \(c\) is \(-2\) (which is negative).

### Conclusion
Based on the slope and y-intercept:
- The slope is positive (\(\frac{3}{2}\)).
- The y-intercept is negative (\(-2\)).

Thus, the correct statement about the graph of the equation \(2y - 3x = -4\) is that it has a positive slope and a negative y-intercept.