Question

Using the graph, derive the equation of the line in slo e-intercept form.
(1 point)
A. y = 3x + 4
B. y = 3x -4
C.y = 3x - 4
D. 3x - y = 4


the dots are at 0, -4 1,-1

Answer 1

To derive the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b) from the coordinates of the points provided.

The two points provided are:
- Point 1: (0, -4)
- Point 2: (1, -1)

1. **Finding the slope (m)**:
The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, we can take \((x_1, y_1) = (0, -4)\) and \((x_2, y_2) = (1, -1)\):
\[
m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3
\]

2. **Finding the y-intercept (b)**:
Since one of the points is (0, -4), the y-intercept (b) is -4.

3. **Putting it together**:
Now, we can write the equation of the line in slope-intercept form:
\[
y = mx + b
\]
Substituting the values we found, we get:
\[
y = 3x - 4
\]

The correct answer from the options given is:
**C. y = 3x - 4**