Question

Use the image to answer the question.
(1, -1), (0, -4)
Using the graph, derive the equation of the line in slope-intercept form.
A. 3x - y = 4
B. y = 3x + 4
C. y = -3x - 4
D. y = 3x - 4

Answer 1

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

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (1, -1) and (0, -4):

\((x_1, y_1) = (1, -1)\)

\((x_2, y_2) = (0, -4)\)

Calculating the slope:

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

Now that we have the slope \( m = 3 \), we can use one of the points to find \( b \), the y-intercept. We can use the point (0, -4):

Since the y-intercept \( b \) occurs where \( x = 0 \), we already have that \( y = -4\) when \( x = 0 \).

Thus, we can write the equation with the slope and y-intercept:

\[
y = 3x - 4
\]

This corresponds to option **D**: \( y = 3x - 4 \).