Question

Derive the equation of the line in slope-intercept form. (1,8) and (0,4)
y=_x+_

Answer 1

To derive the equation of the line in slope-intercept form \( y = mx + b \), we first need to find the slope \( m \) using the two points given: \((1, 8)\) and \((0, 4)\).

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 \((1, 8)\) and \((0, 4)\):

\[
m = \frac{4 - 8}{0 - 1} = \frac{-4}{-1} = 4
\]

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 \((0, 4)\), where \( x = 0 \) and \( y = 4 \).

In slope-intercept form \( y = mx + b\):

\[
4 = 4(0) + b
\]

This simplifies to:

\[
4 = b
\]

Now we can write the equation of the line:

\[
y = 4x + 4
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = 4x + 4
\]

So the final answer is:

\[
y = 4x + 4
\]