Question
Use the image to answer the question.
A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 5 comma 1 right parenthesis.
Is this the correct graph of the equation y=15x?
(1 point)
Responses
Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m=riserun=15.
Yes, it is the correct graph because the ordered pair left parenthesis 0 comma 0 right parenthesis satisfies the equation and the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction .
No, it is not the correct graph because the slope m=riserun=15.
No, it is not the correct graph because the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction .
Yes, it is the correct graph because the slope =51.
Yes, it is the correct graph because the slope equals Start Fraction 5 over 1 End Fraction .
No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=15x
A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 5 comma 1 right parenthesis.
Is this the correct graph of the equation y=15x?
(1 point)
Responses
Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m=riserun=15.
Yes, it is the correct graph because the ordered pair left parenthesis 0 comma 0 right parenthesis satisfies the equation and the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction .
No, it is not the correct graph because the slope m=riserun=15.
No, it is not the correct graph because the slope m equals Start Fraction rise over run End Fraction equals Start Fraction 1 over 5 End Fraction .
Yes, it is the correct graph because the slope =51.
Yes, it is the correct graph because the slope equals Start Fraction 5 over 1 End Fraction .
No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=15x
Answers
GPT-4o mini
To determine if the graph is correct for the equation \( y = 15x \), we need to analyze the points provided and the slope of the line.
1. **Check the points**: The two plotted points are \( (0, 0) \) and \( (5, 1) \).
- The point \( (0, 0) \) does satisfy the equation \( y = 15x \) because substituting \( x = 0 \) gives \( y = 15 \cdot 0 = 0 \).
- For the point \( (5, 1) \), substituting \( x = 5 \) gives \( y = 15 \cdot 5 = 75 \), which does **not** match the \( y \)-coordinate of 1.
2. **Calculate the slope**:
- The slope \( m \) between the two points can be calculated using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):
\[
m = \frac{1 - 0}{5 - 0} = \frac{1}{5}
\]
Given that the slope from the points is \( \frac{1}{5} \), which is significantly different from the slope of 15 that would be indicated by the equation \( y = 15x \).
Based on this analysis, the correct answer is:
**No, it is not the correct graph because the slope \( m = \frac{1}{5} \).**
1. **Check the points**: The two plotted points are \( (0, 0) \) and \( (5, 1) \).
- The point \( (0, 0) \) does satisfy the equation \( y = 15x \) because substituting \( x = 0 \) gives \( y = 15 \cdot 0 = 0 \).
- For the point \( (5, 1) \), substituting \( x = 5 \) gives \( y = 15 \cdot 5 = 75 \), which does **not** match the \( y \)-coordinate of 1.
2. **Calculate the slope**:
- The slope \( m \) between the two points can be calculated using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \):
\[
m = \frac{1 - 0}{5 - 0} = \frac{1}{5}
\]
Given that the slope from the points is \( \frac{1}{5} \), which is significantly different from the slope of 15 that would be indicated by the equation \( y = 15x \).
Based on this analysis, the correct answer is:
**No, it is not the correct graph because the slope \( m = \frac{1}{5} \).**