Use the image to answer the question.

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.

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 .

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 given line is the correct graph of the equation \( y = -13x + 4 \), we can analyze both the slope and the y-intercept.

1. The equation \( y = -13x + 4 \) has a y-intercept of \( (0, 4) \). This means that the line should cross the y-axis at the point (0, 4).

2. The coordinates of the plotted points given are:

   • Point A: \( (0, 3) \)
   • Point B: \( (3, 2) \)

3. To find the slope between these two points, we use the slope formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 0} = \frac{-1}{3} \] This indicates that the graph has a negative slope, which is inconsistent with the slope of \( -13 \) from the equation.

4. Therefore, since the graph has a y-intercept of \( (0, 3) \) instead of \( (0, 4) \) and has a negative slope that is different from the one calculated from the equation, we conclude that:

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