A pediatrician records the age x (in yr) and average height y (in inches) for girls between the ages of 2 and 10.a. Use the points (2, 37) and (6, 50) to write a linear model for these data.b. Use the model to forecast the average height of 11-yr-old girls.Select one:a. a. y = 3.25x + 30.5; b. 66.25 in.b. a. y = 3.25x + 30.5; b. 67.25 in.c. a. y = 3x + 29.5; b. 63.25 in.d. a. y = 3x + 29.5; b. 62.5 in.
Question
A pediatrician records the age x (in yr) and average height y (in inches) for girls between the ages of 2 and 10.a. Use the points (2, 37) and (6, 50) to write a linear model for these data.b. Use the model to forecast the average height of 11-yr-old girls.Select one:a. a. y = 3.25x + 30.5; b. 66.25 in.b. a. y = 3.25x + 30.5; b. 67.25 in.c. a. y = 3x + 29.5; b. 63.25 in.d. a. y = 3x + 29.5; b. 62.5 in.
Solution
a. To write a linear model for these data, we first need to find the slope of the line that passes through the points (2, 37) and (6, 50). The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula, we get:
m = (50 - 37) / (6 - 2) = 13 / 4 = 3.25
The equation of a line is given by y = mx + b, where b is the y-intercept. To find b, we can substitute one of the points and the slope into the equation. Using the point (2, 37), we get:
37 = 3.25 * 2 + b 37 = 6.5 + b b = 37 - 6.5 = 30.5
So, the linear model is y = 3.25x + 30.5.
b. To forecast the average height of 11-year-old girls, we substitute x = 11 into the model:
y = 3.25 * 11 + 30.5 = 35.75 + 30.5 = 66.25 inches.
So, the correct answer is a. a. y = 3.25x + 30.5; b. 66.25 in.
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