Question

Use the graph to derive the equation of the line in slope-intercept form
The graph has a dotted line with (0,-2) (1,3)
Y = _ x -_

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 \( b \).

1. **Find the slope \( m \)**:
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (0, -2) \) and \( (1, 3) \):
\[
m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5
\]

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

3. **Combine to form the equation**:
Now we can substitute \( m \) and \( b \) into the slope-intercept form:
\[
y = 5x - 2
\]

Thus, the equation of the line is:
\[
Y = 5x - 2
\]