To find the equation of the line in slope-intercept form \(y = mx + b\), we first need to calculate the slope \(m\) using the two points given: \((0, -2)\) and \((3, 0)\).
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \((0, -2)\) and \((3, 0)\):
- \(x_1 = 0\), \(y_1 = -2\)
- \(x_2 = 3\), \(y_2 = 0\)
Now, plug the values into the slope formula:
\[ m = \frac{0 - (-2)}{3 - 0} = \frac{2}{3} \]
Now that we have the slope \(m = \frac{2}{3}\), we can use one of the points (either one will work, but we will use \((0, -2)\) since it makes finding \(b\) simpler) to find the y-intercept \(b\).
The y-intercept \(b\) is the \(y\)-value when \(x = 0\), which is given as \(-2\). Therefore, \(b = -2\).
Now we can write the equation of the line in slope-intercept form:
\[ y = \frac{2}{3}x - 2 \]
So, the equation of the line is:
\[ \boxed{y = \frac{2}{3}x - 2} \]
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