Question

Use the image to answer the question.
(1, 0), (0, -3)
What is the equation o the line the form y = mx + b?
A. y = -3x - 3
B. y = 3x + 3
C. y = 3x - 3
D. -3x - y = 3

Answer 1

To find the equation of the line in the form \( y = mx + b \), we can use the two points given: \( (1, 0) \) and \( (0, -3) \).

1. **Calculate the slope (m)**:
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (1, 0) \) and \( (0, -3) \):
- \( (x_1, y_1) = (1, 0) \)
- \( (x_2, y_2) = (0, -3) \)

Plugging in the values:
\[
m = \frac{-3 - 0}{0 - 1} = \frac{-3}{-1} = 3
\]

2. **Find the y-intercept (b)**:
The y-intercept \( b \) can be found from one of the points. Since the second point is \( (0, -3) \), it directly gives us the y-intercept:
\[
b = -3
\]

3. **Write the equation**:
Now, substituting \( m \) and \( b \) into the line equation \( y = mx + b \):
\[
y = 3x - 3
\]

Therefore, the correct equation of the line is:
**C. \( y = 3x - 3 \)**.