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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

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.

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.

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 .
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Answer 1

To determine whether the specified line on the graph represents the equation \(y = -13x + 4\), we should evaluate a few key aspects of the equation and the points provided.

1. Identify the y-intercept: The y-intercept of the line \(y = -13x + 4\) is the point where \(x = 0\). Plugging \(x = 0\) into the equation, we find: \[ y = -13(0) + 4 = 4 \] Thus, the y-intercept is \((0, 4)\).

2. Check the slope: The slope of the line \(y = -13x + 4\) is \(-13\), which is negative. This means the graph should be descending from left to right.

3. Check the plotted points: The coordinates of the plotted points on the graph are \((0, 3)\) and \((3, 2)\).

   • The point \((0, 3)\) indicates a different y-intercept than the one calculated from the equation, which is supposed to be \((0, 4)\).
   • A line passing through \((0, 3)\) would indicate a different linear equation.

Given these evaluations:

• Since the graph indicated a y-intercept of \((0, 3)\) rather than \((0, 4)\) and the slope is different (should be negative for the equation given), we conclude that:

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