Question

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 ?(1 point)
Responses

No, it is not the correct graph because this graph has a positive slope.
No, it is not the correct graph because this graph has a positive slope.

Yes, it is the correct graph because this graph has a y-intercept of (0,4).
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 4 right parenthesis .

Yes, it is the correct graph because this graph has a y-intercept of (0,3).
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 3 right parenthesis .

No, it is not the correct graph because this graph used (0,3) as the y-intercept.
No, it is not the correct graph because this graph used left parenthesis 0 comma 3 right parenthesis as the y -intercept.
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Answer 1

To determine if the graph corresponds to the equation \( y = -\frac{1}{3}x + 4 \), we need to analyze the components of the equation.

1. Slope: The slope of the line in the equation \( y = -\frac{1}{3}x + 4 \) is \(-\frac{1}{3}\), which is negative. This indicates that the line should be decreasing.

2. Y-intercept: The y-intercept of this equation is 4, which means the line crosses the y-axis at the point (0, 4).

The points plotted as stated in the question are (0, 3) and (3, 2).

• At (0, 3), the graph shows the line crossing the y-axis at 3, not 4.
• At (3, 2), if we substitute \(x = 3\) into \(y = -\frac{1}{3}(3) + 4\), we get \(y = -1 + 4 = 3\), not 2.

Thus, since the line passes through (0, 3) instead of (0, 4) and the slope does not match, the graph does not represent the equation \(y = -\frac{1}{3}x + 4\).

The appropriate response is:

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