To derive the equation of the line in slope-intercept form \(y = mx + b\) using the points (1, 8) and (0, 4), let's first 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 (1, 8) as \((x_1, y_1)\) and (0, 4) as \((x_2, y_2)\):
\[ m = \frac{4 - 8}{0 - 1} = \frac{-4}{-1} = 4 \]
Now that we have the slope \(m = 4\), we will use one of the points to find the y-intercept \(b\). We can use the point (0, 4), which is already in the form \((x, y)\).
In slope-intercept form:
\[ y = mx + b \]
Substituting \(m = 4\) and using the point (0, 4):
\[ 4 = 4(0) + b \] \[ b = 4 \]
Now we have both \(m\) and \(b\). The slope-intercept form of the line is:
\[ y = 4x + 4 \]
This is the equation of the line that passes through the points (1, 8) and (0, 4).