To find the equation of a line in slope-intercept form \(y = mx + b\), we first need to determine the slope \(m\) using the two given points: (3, 0) and (0, -2).
The formula for 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 (3, 0) \((x_1, y_1)\) and (0, -2) \((x_2, y_2)\):
\[ m = \frac{-2 - 0}{0 - 3} = \frac{-2}{-3} = \frac{2}{3} \]
Now that we have the slope \(m = \frac{2}{3}\), we can use one of the points to find the y-intercept \(b\). We will use the point (0, -2), where \(x = 0\) and \(y = -2\).
In the slope-intercept form, when \(x = 0\), \(b\) is the y-coordinate:
\[ b = -2 \]
Now we have both \(m\) and \(b\). We can write the equation of the line:
\[ y = \frac{2}{3}x - 2 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = \frac{2}{3}x - 2 \]