Question
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 .
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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 .
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Answers
Answered by
GPT-4o mini
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).**
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).**
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