A coordinate plane with a line passing through (0, negative 3), (2, 0), and (4, 3).

To find the equation of the line that passes through the points (0, -3), (2, 0), and (4, 3), we can first determine the slope of the line using the points (0, -3) and (2, 0).

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (0, -3) and (2, 0):

\[ m = \frac{0 - (-3)}{2 - 0} = \frac{3}{2} \]

Now that we have the slope, we can use the point-slope form of the equation of a line, which is given by:

\[ y - y_1 = m(x - x_1) \]

Using the point (0, -3):

\[ y - (-3) = \frac{3}{2}(x - 0) \]

This simplifies to:

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

Subtracting 3 from both sides gives us:

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

Now let's convert this to standard form. To do this, we can multiply the entire equation by 2 to eliminate the fraction:

\[ 2y = 3x - 6 \]

Rearranging gives:

\[ 3x - 2y - 6 = 0 \]

Next, we can check the given options to see which represents this line.

Testing the functions provided:

1. –3x + 2 = y: Rearranging this gives \(y = -3x + 2\).
2. –x + 2 = y: Rearranging this gives \(y = -x + 2\).
3. x – 3 = y: Rearranging this gives \(y = x - 3\).
4. 2x – 3 = y: Rearranging this gives \(y = 2x - 3\).

None of these options match \(y = \frac{3}{2}x - 3\) directly, but the slope gives information about the line's steepness. Let's check the values one by one:

• For \(y = 2x - 3\):
  • At \(x = 0\), \(y = 2(0) - 3 = -3\) (matches \((0, -3)\)).
  • At \(x = 2\), \(y = 2(2) - 3 = 1\) (doesn't match \((2, 0)\)).
  • At \(x = 4\), \(y = 2(4) - 3 = 5\) (doesn't match \((4, 3)\)).

None of them seem to satisfy all three points.

Let's focus on the slope \( \frac{3}{2} \) and intercept \( -3\).

To correct the error in comparing slopes and confirm:

• The changes in \(y\) and \(x\) from \(y=-3\) to \(y=3\) at increments gives \(x\) changes of \(4\) for \(y\) to change by \(6\) (from \(−3\) to \(3\)) as evaluated:

Conclusively from all options provided and possible mistakes in graphical interpretation, the actual points and slope check shows:

None fit perfectly; the closest match given the slope structure and solving \(2x\) shows error. Thus I urge rescinded expression or re-evaluating mathematical errors for slope inferred in closest to the existing \(g(y)\) as future expression leads imply approximates in graphical coordinates miscue corrections.

Final acknowledgement recommends evaluating other options as no direct match under standard form appears feasible here.