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?
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 (1.88) indicates how much the height (h) changes for each one-unit increase in femur length (f). This means that for every additional inch in femur length, the height increases by 1.88 inches.
This statement incorrectly interprets the slope as a value related to femur length at a specific height. Instead, the slope describes the relationship between changes in femur length and changes in height, not a specific value at a certain height.
This statement accurately describes the slope of the equation. The slope of 1.88 signifies that for each 1-inch increase in femur length, the height increases by 1.88 inches, which is the correct interpretation of the slope in this linear relationship.
This statement reverses the relationship described by the slope. It incorrectly states that the slope measures the change in femur length per inch of height, whereas the slope actually measures the change in height per inch of femur length.
This statement misidentifies the slope as 32, which is actually the y-intercept of the equation, not the slope. The y-intercept indicates the height when the femur length is zero, not the change in height per change in femur length.
This statement incorrectly identifies the slope as 32 and misrepresents the concept of slope. The value of 32 is the y-intercept, indicating height at a femur length of zero, not the slope or its relationship to femur length.
The slope of a linear equation provides essential insights into the relationship between two variables. In this case, a slope of 1.88 signifies that height increases by 1.88 inches for each additional inch of femur length. Understanding this relationship is crucial in contexts such as biomechanics or health assessments, where measurements of body proportions are analyzed.
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