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

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.

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 .
Skip to navigation

1 answer

To determine whether the graph represents the equation \( y = -13x + 4 \), we first need to check what the y-intercept of this equation is.

The equation \( y = -13x + 4 \) has a y-intercept at \( (0, 4) \) since when \( x = 0 \): \[ y = -13(0) + 4 = 4. \]

The plotted points given in the question are \( (0, 3) \) and \( (3, 2) \). The y-intercept indicated by the graph is \( (0, 3) \), which does not match the y-intercept of the equation \( (0, 4) \).

Additionally, the slope of the line can be calculated using the two points. The slope \( m \) between the points \( (0, 3) \) and \( (3, 2) \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 0} = \frac{-1}{3}. \] Since the slope \( -13 \) from the equation is significantly steeper than \( -\frac{1}{3} \), this further indicates that the graph does not represent the given equation.

Given all this information, the appropriate response would be:

No, it is not the correct graph because this graph has a y-intercept of (0, 3).