Question

Use the image to answer the question.
(1, 8), (0, 4)
Derive the equation of the line in slope-intercept form.
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Answer 1

To derive the equation of the line in slope-intercept form (y = mx + b) using the points (1, 8) and (0, 4), we'll follow these steps:

1. **Find the slope (m)**:
The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Let \( (x_1, y_1) = (1, 8) \) and \( (x_2, y_2) = (0, 4) \):
\[
m = \frac{4 - 8}{0 - 1} = \frac{-4}{-1} = 4
\]

2. **Use the slope and one of the points to find the y-intercept (b)**:
We can use the y-intercept point (0, 4) which suggests that when \( x = 0 \), \( y = 4 \). Thus, \( b = 4 \).

3. **Write the equation**:
Now, we can plug the slope and y-intercept into the slope-intercept form:
\[
y = mx + b
\]
Substituting \( m = 4 \) and \( b = 4 \):
\[
y = 4x + 4
\]

Thus, the equation of the line in slope-intercept form is:
\[
y = 4x + 4
\]