Question

Using the graph, derive the equation of the line in slope-intercept form.

Graph is (1, -1) and (0, -4)

Answer 1

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

1. **Calculate the slope (m):**
The formula for the slope between two points (x1, y1) and (x2, y2) is:

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

Let's substitute the points into this formula:

- Point 1 (x1, y1) = (1, -1)
- Point 2 (x2, y2) = (0, -4)

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

So, the slope \( m = 3 \).

2. **Use the slope to find the y-intercept (b):**
The y-intercept (b) can be directly obtained from the point (0, -4), which corresponds to the y-coordinate when x = 0. Thus, \( b = -4 \).

3. **Write the equation in slope-intercept form:**
Now that we have both the slope (m) and the y-intercept (b), we can write the equation of the line:

\[
y = 3x - 4
\]

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

\[
y = 3x - 4
\]