please help!
The following equation can be used to predict the average height of boys anywhere between birth and 15
years old: y = 2.79x +25.64 where x is the age (in years) and y is the height (in inches).
a. What does the slope represent in this problem? Interpret it in context.
b. What does the y-intercept represent in this problem? Interpret it in context.
slope is the boys' growth rate, inches/year
the y-intercept is where x=0, that is, the height at birth. Wow! 25.64 inches at birth! Probably just a fudge factor so that height in subsequent years is a decent approximation.
thank you so much!
A)2.79 height
B) 25.64
To answer these questions, let's first understand the equation and its components:
The equation given is: y = 2.79x + 25.64
a. The slope (which is represented by 2.79 in this equation) represents the rate of change between the age (x) and the height (y) of boys. Specifically, it tells us how much the height increases (or decreases) on average for every one year increase in age. In this case, since the slope is positive (2.79), it indicates that, on average, the height of boys increases by 2.79 inches for each year they age.
b. The y-intercept (represented by 25.64 in this equation) represents a starting point on the graph. In the context of this problem, it tells us the average height of boys at birth (age 0). In other words, when x = 0 (birth), the value of y (height) will be equal to the y-intercept. Therefore, the y-intercept of 25.64 inches suggests that the average height of boys at birth is approximately 25.64 inches.
To summarize, the slope represents the average increase in height for each one-year increase in age, while the y-intercept represents the average height of boys at birth.