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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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1 answer

To determine whether the given graph represents the equation \( y = -13x + 4 \), we need to identify the y-intercept of this equation and check the slope.

  1. Identifying the Y-Intercept: The y-intercept of the line \( y = -13x + 4 \) is the point where \( x = 0 \): \[ y = -13(0) + 4 = 4 \] So, the y-intercept is \( (0, 4) \).

  2. Checking the Slope: The slope of the equation \( y = -13x + 4 \) is -13, which is a negative slope, meaning the line slopes downward from left to right.

  3. Analyzing the Points: The plotted points are \( (0, 3) \) and \( (3, 2) \). The y-intercept based on the graph is \( (0, 3) \), which does not match the calculated y-intercept of \( (0, 4) \).

Given these observations, the correct response would be:

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