Question
Graphing Proportional Relationships Quick Check 5 of 55 of 5 Items Question Use the image to answer the question. 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 . No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=15x No, it is not the correct graph because the ordered pair left parenthesis 1 comma 5 right parenthesis is not a point on the graph of y equals Start Fraction 1 over 5 End Fraction x Yes, it is the correct graph because the slope =51 .
Answers
GPT-4o mini
To determine if the graph is correct for the equation \( y = 15x \), we need to evaluate a few key characteristics:
1. **Check the y-intercept**: The equation \( y = 15x \) has a y-intercept at (0,0). This means that the graph must pass through the origin.
2. **Check the slope**: The slope \( m \) of the line is 15, which means that for every 1 unit increase in \( x \), \( y \) should increase by 15 units.
3. **Check ordered pairs**: You can also evaluate other points on the graph. For example, if \( x = 1 \), then \( y = 15(1) = 15 \). Thus, the point (1, 15) should be on the graph.
Now we can evaluate the responses given:
- The first response states that the slope is \( \frac{\text{rise}}{\text{run}} = 15 \) and that the point (0, 0) satisfies the equation, which is accurate if the graph does pass through the origin and has the correct slope.
- The second response claims that the slope is \( \frac{1}{5} \), which is incorrect for the equation \( y = 15x \).
- The third and fourth responses also incorrectly quote the slope \( \frac{1}{5} \) for \( y = 15x \), so they are incorrect.
- The last two responses seem to have a misunderstanding regarding the points listed. The equation \( y = 15x \) should have (1, 15) instead of (1, 5).
Based on this evaluation, the correct response would be:
**No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of \( y = 15x \).**
This response reflects the fact that the slope is not accurate and misrepresented by the graph.
1. **Check the y-intercept**: The equation \( y = 15x \) has a y-intercept at (0,0). This means that the graph must pass through the origin.
2. **Check the slope**: The slope \( m \) of the line is 15, which means that for every 1 unit increase in \( x \), \( y \) should increase by 15 units.
3. **Check ordered pairs**: You can also evaluate other points on the graph. For example, if \( x = 1 \), then \( y = 15(1) = 15 \). Thus, the point (1, 15) should be on the graph.
Now we can evaluate the responses given:
- The first response states that the slope is \( \frac{\text{rise}}{\text{run}} = 15 \) and that the point (0, 0) satisfies the equation, which is accurate if the graph does pass through the origin and has the correct slope.
- The second response claims that the slope is \( \frac{1}{5} \), which is incorrect for the equation \( y = 15x \).
- The third and fourth responses also incorrectly quote the slope \( \frac{1}{5} \) for \( y = 15x \), so they are incorrect.
- The last two responses seem to have a misunderstanding regarding the points listed. The equation \( y = 15x \) should have (1, 15) instead of (1, 5).
Based on this evaluation, the correct response would be:
**No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of \( y = 15x \).**
This response reflects the fact that the slope is not accurate and misrepresented by the graph.