Question

Write the equation of the line in slope-intercept form. Points are (0, -2) and (3, 0)

Answer 1

To find the equation of the line in slope-intercept form \(y = mx + b\), we start by determining the slope \(m\) using the two points given: (0, -2) and (3, 0).

1. **Calculate the slope \(m\)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{3 - 0} = \frac{0 + 2}{3} = \frac{2}{3}
\]

2. **Use one point to solve for the y-intercept \(b\)**. We can use the point (0, -2):
\[
y = mx + b \rightarrow -2 = \frac{2}{3}(0) + b \rightarrow -2 = b
\]

3. **Now we have both \(m\) and \(b\)**:
- Slope \(m = \frac{2}{3}\)
- Y-intercept \(b = -2\)

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

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