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=−1/3 x+4 ?(1 point)
Responses

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 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 .

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

Answer 1

To determine whether the line connecting the points (0, 3) and (3, 2) corresponds to the equation \( y = -\frac{1}{3}x + 4 \), we need to analyze both the slope of the line formed by those points and the y-intercept.

1. **Calculate the Y-Intercept**:
The equation \( y = -\frac{1}{3}x + 4 \) has a y-intercept of (0, 4), as when \( x = 0 \), \( y \) equals 4.

2. **Check the Given Points**:
The points provided are (0, 3) and (3, 2). Here, at \( x = 0 \), the value of \( y \) is 3, which indicates that the y-intercept of this graph is (0, 3) rather than (0, 4).

3. **Calculate the Slope**:
The slope between the two points can be calculated as follows:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 0} = \frac{-1}{3}
\]
Since the slope is negative, it matches the coefficient in the given equation.

4. **Conclusion**:
The correct y-intercept for the graph based on the provided points (0, 3) and (3, 2) is (0, 3), not (0, 4) as stated in the equation \( y = -\frac{1}{3}x + 4 \).

Therefore, the answer is:

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