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=−13x+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.
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 represents the equation \( y = -13x + 4 \), we need to evaluate both the y-intercept and the slope.

1. **Y-Intercept**: For the equation \( y = -13x + 4 \), the y-intercept occurs when \( x = 0 \).
\[
y = -13(0) + 4 = 4
\]
Thus, the y-intercept is \( (0, 4) \).

2. **Slope**: The slope \( -13 \) indicates that for each unit increase in \( x \), \( y \) decreases by \( 13 \).

Given the plotted points \( (0, 3) \) and \( (3, 2) \):

- The point \( (0, 3) \) indicates that the y-intercept used in the graph is \( 3 \), not \( 4 \) as required by the equation.
- The slope between \( (0, 3) \) and \( (3, 2) \) can be calculated:
\[
\text{slope} = \frac{2 - 3}{3 - 0} = \frac{-1}{3}
\]
This slope is positive, unlike the negative slope that \( -13 \) would indicate.

Based on this analysis, the correct response is:

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