Question

Use the image to answer the question.
(3, 0), (0, -2)
Write the equation of the line in slope-intercept form.
__

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we first need to find the slope (m) between the two points (3, 0) and (0, -2).

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, (x1, y1) = (3, 0) and (x2, y2) = (0, -2).

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

2. **Use the slope and one of the points to find the y-intercept (b)**. We can use the point (3, 0):
\[
y = mx + b
\]
Plugging in the values:
\[
0 = \frac{2}{3}(3) + b
\]
\[
0 = 2 + b
\]
\[
b = -2
\]

3. **Now write the equation** in slope-intercept form:
\[
y = \frac{2}{3}x - 2
\]

Thus, the equation of the line in slope-intercept form is:
\[
y = \frac{2}{3}x - 2
\]