Asked by Jayla
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
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.
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 .
No, it is not the correct graph because this graph used (0,3)
as the y
-intercept.
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.
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 .
No, it is not the correct graph because this graph used (0,3)
as the y
-intercept.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine whether the graph represents the equation \( y = -13x + 4 \), we need to analyze the slope and y-intercept of the line.
1. **Y-Intercept**: The y-intercept occurs when \( x = 0 \). Plugging in \( x = 0 \) into the equation \( y = -13(0) + 4 \), we find:
\[
y = 4
\]
Therefore, the y-intercept is \( (0, 4) \).
2. **Slope**: The slope of the line \( y = -13x + 4 \) is \(-13\), which is negative. A negative slope means that the line decreases as \( x \) increases.
3. **Checking the Points**: The two plotted points are \( (0, 3) \) and \( (3, 2) \).
- The point \( (0, 3) \) does not match the y-intercept we calculated, which is \( (0, 4) \).
- Additionally, checking the second point:
- When \( x = 3 \):
\[
y = -13(3) + 4 = -39 + 4 = -35
\]
The point \( (3, 2) \) does not lie on the line either.
Based on this analysis, the graph does not correctly represent the equation \( y = -13x + 4 \), as it uses the point \( (0, 3) \) as the y-intercept and not \( (0, 4) \).
Therefore, the appropriate response would be:
**No, it is not the correct graph because this graph used \( (0, 3) \) as the y-intercept.**
1. **Y-Intercept**: The y-intercept occurs when \( x = 0 \). Plugging in \( x = 0 \) into the equation \( y = -13(0) + 4 \), we find:
\[
y = 4
\]
Therefore, the y-intercept is \( (0, 4) \).
2. **Slope**: The slope of the line \( y = -13x + 4 \) is \(-13\), which is negative. A negative slope means that the line decreases as \( x \) increases.
3. **Checking the Points**: The two plotted points are \( (0, 3) \) and \( (3, 2) \).
- The point \( (0, 3) \) does not match the y-intercept we calculated, which is \( (0, 4) \).
- Additionally, checking the second point:
- When \( x = 3 \):
\[
y = -13(3) + 4 = -39 + 4 = -35
\]
The point \( (3, 2) \) does not lie on the line either.
Based on this analysis, the graph does not correctly represent the equation \( y = -13x + 4 \), as it uses the point \( (0, 3) \) as the y-intercept and not \( (0, 4) \).
Therefore, the appropriate response would be:
**No, it is not the correct graph because this graph used \( (0, 3) \) as the y-intercept.**
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