Question

Use the image to answer the question.
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 3 comma 2 right parenthesis.
Is this the correct graph of y=−1/3x + 4 ?

A. No, it is not the correct graph because this graph has a positive slope.
B. No, it is not the correct graph because this graph used (0,3) as the y-intercept.
C. Yes, it is the correct graph because this graph has a y-intercept of (0,4).
D. Yes, it is the correct graph because this graph has a y-intercept of (0,3).

Answer 1

To determine if the given line is the correct graph of the equation \( y = -\frac{1}{3}x + 4 \), we can analyze the slope and y-intercept.

1. **Identify the y-intercept**: The y-intercept from the equation \( y = -\frac{1}{3}x + 4 \) is at the point \( (0, 4) \).

2. **Examine the plotted points**: The two plotted points given are \( (0, 3) \) and \( (3, 2) \). The first point \( (0, 3) \) shows a y-value of 3, indicating that the graph intersects the y-axis at this point, not at 4.

3. **Determine the slope**: The slope can be calculated using the two points:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 0} = \frac{-1}{3}
\]
The slope here is indeed \(-\frac{1}{3}\).

Now, let's summarize the analysis:

- The graph does have the correct slope of \(-\frac{1}{3}\).
- However, it does **not** have the correct y-intercept as it should be \( (0, 4) \) instead of \( (0, 3) \).

Given this information, the correct statement is:

**B. No, it is not the correct graph because this graph used (0,3) as the y-intercept.**