Question

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

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 given points \((1, -1)\) 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 \((1, -1)\) as \((x_1, y_1)\) and \((0, -4)\) as \((x_2, y_2)\):

\[
m = \frac{-4 - (-1)}{0 - 1} = \frac{-4 + 1}{-1} = \frac{-3}{-1} = 3
\]

So the slope \(m = 3\).

Next, we can use one of the points to find the y-intercept \(b\). We'll use the point \((0, -4)\):

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

Substituting \(m = 3\) and the point \((0, -4)\):

\[
-4 = 3(0) + b
\]

This simplifies to:

\[
-4 = b
\]

So the y-intercept \(b = -4\).

Now, we can put \(m\) and \(b\) together to write the equation of the line in slope-intercept form:

\[
y = 3x - 4
\]

This is the equation of the line that passes through the points \((1, -1)\) and \((0, -4)\).