Question

Using the graph, 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 \( y = mx + b \) using the points \( (3, 0) \) and \( (0, -2) \), follow these steps:

1. **Find the slope (m)**:
The formula for the 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 \( (3, 0) \) and \( (0, -2) \):
- Let \( (x_1, y_1) = (3, 0) \)
- Let \( (x_2, y_2) = (0, -2) \)

Now, calculate the slope:
\[
m = \frac{-2 - 0}{0 - 3} = \frac{-2}{-3} = \frac{2}{3}
\]

2. **Use the slope and one of the points to find the y-intercept (b)**:
We can use the point \( (0, -2) \) since it directly gives us the y-intercept. The y-intercept \( b \) is the value of \( y \) when \( x = 0 \):
\[
b = -2
\]

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

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