Dean wrote the equation y=13x to show the relationship between the number of hours, x , and the number of miles he can ride on his bike, y . He used his equation to calculate how many miles he could ride his bike in 5 hours: yyy=13x=13×5=65 Dean determined that he could ride 65 miles in 5 hours.What are the two quantities being related in this problem? How are they related? What is another way Dean could have shown the relationship between the two quantities in this problem besides an equation? How did Dean demonstrate his ability to reason abstractly and quantitatively?
The two quantities being related in this problem are the number of hours (x) and the number of miles (y) Dean can ride on his bike. They are related by the equation y = 13x, which means that for every hour Dean rides, he can travel 13 miles.
Another way Dean could have shown the relationship between the two quantities is by creating a table or a graph. He could have made a table with different values for x (number of hours) and calculated the corresponding values for y (number of miles). This would help him visualize how the miles increase as the hours increase.
Dean demonstrated his ability to reason abstractly and quantitatively by successfully using the equation to calculate how many miles he could ride in 5 hours. He understood the equation and was able to apply it to a specific situation. This shows his ability to think abstractly (using the equation as a general representation of the relationship) and quantitatively (plugging in specific values and calculating a result).
The two quantities being related in this problem are the number of hours (x) and the number of miles Dean can ride his bike (y). They are related by the equation y = 13x, which states that for every hour (x), Dean can ride 13 times that number of miles (y).
Another way Dean could have shown the relationship between the two quantities is by creating a table. He could list the number of hours in one column and the corresponding number of miles in another column. Then, using the equation y = 13x, he could calculate the miles for different numbers of hours and fill in the table.
Dean demonstrated his ability to reason abstractly and quantitatively by using the equation y = 13x to calculate the number of miles he could ride in 5 hours. By substituting x = 5 into the equation, he obtained y = 13 * 5 = 65. This shows that Dean can understand the abstract relationship between the hours and miles and apply quantitative reasoning to solve the problem.
The two quantities being related in this problem are the number of hours, represented by x, and the number of miles Dean can ride his bike, represented by y. They are related in a linear manner, with the equation y = 13x. This means that for every hour Dean rides his bike, he can ride 13 miles.
Another way Dean could have shown the relationship between the two quantities is by creating a table or a graph. With a table, he could list the number of hours (x) in one column and the corresponding number of miles (y) in another column. By plugging in different values for x and using the equation y = 13x to find the corresponding y-values, he could create a table showing the relationship.
To demonstrate his ability to reason abstractly and quantitatively, Dean used his equation to calculate how many miles he could ride his bike in 5 hours. By substituting x = 5 into the equation y = 13x, he found y = 13 × 5 = 65. This shows that Dean was able to use logical reasoning and quantitative thinking to solve the problem and determine that he could ride 65 miles in 5 hours.