To write the equation of the line in slope-intercept form (y = mx + b) using the points (3, 0) and (0, -2), we first need to calculate the slope (m) of the line.
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:
- \((x_1, y_1) = (3, 0)\)
- \((x_2, y_2) = (0, -2)\)
We can plug the coordinates into the formula:
\[ m = \frac{-2 - 0}{0 - 3} = \frac{-2}{-3} = \frac{2}{3} \]
Now that we have the slope \(m = \frac{2}{3}\), we can use one of the points to find the y-intercept (b). We'll use the point (0, -2):
Since the point (0, -2) is already in the form (0, b), we can see that the y-intercept \(b = -2\).
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 in slope-intercept form is:
\[ y = \frac{2}{3}x - 2 \]