Final answer:
The linear equations for the Norfolk pine growth, Cairn terrier weight loss, and airplane descent are y = 18x + 18, y = -2x + 30, and y = -500x + 3000, respectively, with slopes 18, -2, and -500, and y-intercepts of 18, 30, and 3000.
Step-by-step explanation:
To write linear equations in slope-intercept form to model each situation presented by the student, we need to identify the value of the slope and the value of the y-intercept for each scenario. The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.
Norfolk Pine Growth
For the Norfolk pine, the growth rate is 1.5 feet per year. Since 1 foot = 12 inches, we convert this to inches per year by multiplying by 12, giving us 18 inches per year. Therefore, the slope (m) is 18. The initial height is 18 inches, which is the y-intercept (b). The linear equation is:
y = 18x + 18, where x is the number of years, and y is the height in inches.
Cairn Terrier Weight Loss
For the Cairn terrier, the weight loss rate is -2 pounds per month, and the initial weight is 30 pounds. The slope is -2, and the y-intercept is 30. The linear equation is:
y = -2x + 30, where x is the number of months, and y is the weight in pounds.
Airplane Descent
An airplane at an altitude of 3000 feet descends at a rate of 500 feet per mile. The slope is -500 (since it's descending), and the y-intercept is 3000 (initial altitude). The linear equation is:
y = -500x + 3000, where x is the distance in miles, and y is the altitude in feet.