Explain why an inverse variation function is not the best model for the data set.
An inverse variation function is not the best model for this data set because in an inverse variation, as x increases, y should decrease. In this data set, as x increases, y also increases. Additionally, for an inverse variation, the product of x and y (xy = k) should be constant. Here, (165)(198) = 32,670 and (170)(204) = 34,680. Since these products are not the same, the data does not represent an inverse variation.
Which did you include in your response?
Explain what type of function is the best model for the data set and justify your choice.
A linear function is the best model for this data set. The ratio of y to x for the ordered pairs is constant, meaning the relationship is a direct variation, which is a type of linear function. Additionally, when the data set is plotted on a graph, the points form a straight line.
What is the slope of the linear function that models the data in the table?The slope is .
1.2
Explain what the slope and y-intercept of the linear model represent in the context of the situation.
The slope of the linear model is 1.2, which represents Alberto's stride length in meters per step; for every additional step per minute, his speed increases by 1.2 meters per minute. The y-intercept is 0, which means that when his stride rate is 0 steps per minute, his speed is 0 meters per minute.
What stride rate would Alberto need in order to match Usain Bolt’s speed in the 100-meter race?
Which did you include in your response?A linear function is the best model.The ratio of y to x for the ordered pairs is constant, so the relationship is a direct variation. A direct variation is a type of linear function.When the data set is plotted, it forms a line.
What is the equation of the linear function that models the data in the table?
Which did you include in your response?
Based on the linear model, which is the best prediction of how long it will take Alberto to finish the 10-kilometer race?
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