Tell whether the two quantities vary directly. Explain your reasoning. 23. the number of ounces of cereal and the number of Calories the cereal contains

Question
Linear equations and graphs
Tell whether the two quantities vary directly. Explain your reasoning. 23. the number of ounces of cereal and the number of Calories the cereal contains

2021-03-07
Two quantities, y and x, vary directly if y=kx where k is the constant of proportionality. The equation y=kx is a linear function with a y-intercept of 0 so two quantities vary directly if their relationship can be modeled by a linear function with a y-intercept of 0.
As the number of ounces of cereal increases, the number of Calories would also increase by a constant rate. The relationship between the two quantities can then be modeled by a linear function since there is a constant rate of change. If there are 0 ounces of cereal, there would be 0 Calories so the linear function has a yy-intercept of 0.
Therefore, the two quantities vary directly.

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Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
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