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

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 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 (0,3)
.

Answer 1

To determine if the graph represents the equation \( y = -13x + 4 \), we should start by identifying the y-intercept and the slope of the line described by the two points given.

1. Identify the y-intercept: The equation \( y = -13x + 4 \) shows that the y-intercept (where \( x = 0 \)) is \( (0, 4) \).

2. Determine the points: The two points plotted on the graph are (0, 3) and (3, 2). The y-coordinate of the point where \( x = 0 \) is 3, which means the y-intercept is (0, 3), not (0, 4).

3. Assess the slope: To find the slope between the points (0, 3) and (3, 2):

   \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 0} = \frac{-1}{3} \]

   The slope of the line is \( -\frac{1}{3} \), which is positive in terms of the equation since \( -13 \) makes the equation negative.

Given the mismatch in the y-intercept and the incorrect slope, the correct conclusion is:

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