Question

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

A. y=3x+4
B. y=3x−4
C. 3x−y=4
D. y=−3x−4

Answer 1

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

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

\[
m = \frac{y2 - y1}{x2 - x1}
\]

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

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

2. **Find the y-intercept (b)**:
Since one of the points is (0, -4), this gives us the y-intercept directly. Here, b = -4.

3. **Write the equation**:
Now that we have the slope (m = 3) and the y-intercept (b = -4), we can write the equation in slope-intercept form:

\[
y = 3x - 4
\]

Thus, the correct answer is **B.** \( y = 3x - 4 \).