To prove her claim that the number of pages read is proportional to the number of minutes spent reading, Sara needs to demonstrate that there is a constant ratio between the two variables. The best way to do this is to show that the relationship can be expressed as a direct proportionality, which is indicated by a straight line passing through the origin when plotted on a graph.
Here's the analysis of each option provided:
A. Place the coordinate pairs in a table and show that they do not create equivalent ratios.
- This would actually disprove her claim, as it implies that the ratios are not consistent.
B. Use the coordinate pairs to show that an equation of the form \(y = kx\) can be written.
- This is a valid approach and supports her claim, as it directly shows the proportional relationship where \(k\) is a constant.
C. List out the coordinate pairs and show that each y-value is a multiple of its associated x-value.
- This would also support her claim and demonstrates the proportional relationship.
D. Plot the coordinate pairs on a graph and show that the points make a straight line through the origin.
- This is also a valid way to prove her claim, as it visually demonstrates the relationship is linear and proportional.
Therefore, the best actions for Sara to take to prove her claim would be:
B, C, and D.
Any of these choices could effectively demonstrate the proportional relationship between the pages read and the minutes spent reading.
1 answer