26. The relationship between h, a person's height in inches, and f, the length in inches of the person's femur, is modeled by the equation: h = 1.88f + 32. Which statement correctly identifies and describes the slope of the equation?
Answer: B
The slope of the equation is 1.88, and it represents the number of inches the height increases for each inch the femur length increases.
In the equation h = 1.88f + 32, the slope of 1.88 indicates that for every one-inch increase in femur length (f), the height (h) increases by 1.88 inches.
A) The slope of the equation is 1.88, and it represents the femur length, in inches, when the height is 32 inches.
This statement is incorrect because the slope does not represent a specific femur length; rather, it quantifies the relationship between femur length and height. The value of 32 is the y-intercept, not the slope.
B) The slope of the equation is 1.88, and it represents the number of inches the height increases for each inch the femur length increases.
This statement is correct. The slope of 1.88 indicates that for each additional inch in femur length, the height increases by 1.88 inches, correctly describing the relationship defined by the equation.
C) The slope of the equation is 1.88, and it represents the number of inches the femur length increases for each inch the height increases.
This option is incorrect because it reverses the relationship described by the slope. The slope indicates how height changes with respect to femur length, not the other way around.
D) The slope of the equation is 32, and it represents the number of inches the height increases for each inch the femur length increases.
This statement is also incorrect as it misidentifies the slope. The slope is 1.88, not 32, which is the y-intercept of the equation.
E) The slope of the equation is 32, and it represents the height, in inches, when the femur length is 1.88 inches.
This statement is incorrect. It confuses the slope with the y-intercept. The value 32 does not represent the slope and does not provide information about the relationship between height and femur length.
Conclusion
The correct answer is B, as it accurately defines the slope of 1.88 in the context of the equation. It properly illustrates how height increases with an increase in femur length, while all other options either misinterpret the slope or incorrectly describe its significance in the relationship between height and femur length.