Question

Use the image to answer the question. Derive the equation of the line in slope-intercept form. 3,0 0,-2

Answer 1

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

1. **Finding the slope (m):**
The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, we can assign:
- \((x_1, y_1) = (3, 0)\)
- \((x_2, y_2) = (0, -2)\)

Plugging in the values:
\[
m = \frac{-2 - 0}{0 - 3} = \frac{-2}{-3} = \frac{2}{3}
\]

2. **Finding the y-intercept (b):**
The y-intercept \(b\) is the value of \(y\) when \(x = 0\). From the second point (0, -2), we see that \(b = -2\).

3. **Constructing the equation:**
Now that we have the slope \(m = \frac{2}{3}\) and the y-intercept \(b = -2\), we can write the equation of the line in slope-intercept form:
\[
y = \frac{2}{3}x - 2
\]

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