Question

A fitness center uses a linear model to advise its customers on what their ideal weight should be based on their height. Height as an input is measured in inches (in), and weight as an output is measured in pounds (lbs).

a) The fitness center told two customers that they are at ideal weights. Customer A is 80 inches tall and weighs 200 pounds. Customer B is 5 feet tall and weighs 100 pounds. Determine the slope of the line that represents the relationship between height and weight that the fitness center uses.
b) Use the slope found in part a and the given information to write the point-slope form of the line. c) convert the point slope form of the line found in part b to its slope intercept form, and use it to graph the linear model the fitness center uses. be sure to plot the points given in part a.
d) What is the y-intercept of this linear relationship? What is the meaning of the y-intercept in this context? Does it make sense?
e) If a customer is 85 inches tall and weighs 250 pounds, would the fitness center tell them that their weight is ideal?
f) What would the fitness center recommend to the customer in part e?

Answer 1

a) The slope of the line that represents the relationship between height and weight is 0.2 (lbs/in).

b) The point-slope form of the line is: y - 200 = 0.2 (x - 80).

c) The slope intercept form of the line is: y = 0.2x + 40. The graph of this line with the two points can be seen below:

d) The y-intercept of this linear relationship is 40. This means that if a person's height is 0 inches, their ideal weight should be 40 pounds. This makes sense as it is not possible to have a negative height.

e) No, the fitness center would not tell the customer in part e that their weight is ideal, as the linear model suggests that their ideal weight should be 200 pounds, which is lower than the 250 pounds they weigh.

f) The fitness center would recommend that the customer in part e should aim to weigh 200 pounds.

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