Question

Using the graph, derive the equation of the line in slope-intercept form (1,8) (0,4)

Answer 1

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).