Use the image to answer the question.

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.