Answer :
Answer:
This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.
One potential confusion students may have follows from the subtle difference between what the car is doing and the idea of slope as the ratio between the change in vertical distance on the graph and the change in horizontal distance on the graph. Because the car is traveling one mile on a down-hill slope, the situation could be represented as a right triangle with a hypotenuse of 5,280 ft and a leg of 250 ft; using the Pythagorean Theorem they would find that the other leg is approximately 5,274 ft. Following through on this interpretation, a student might conclude that the car travels a horizontal distance of approximately 5,274 ft for every 250 ft in vertical distance and arrive at a slope of approximately -0.047. While this is, in some sense, the slope of the hill, it is not the slope of the function as described. This interpretation yields numbers that are very close to the situation described in the task, yet conceptually different since the distance traveled by the car would now be expressed in terms of horizontal distance traveled as opposed to distance along the slope of the hill to compute the elevation. If students do indeed pursue this line of reasoning, the task provides an opportunity to compare and contrast the graph of the function and what it represents with a drawing of the hill and the vertical and horizontal distances traversed with each mile down the slope.
Step-by-step explanation:
From the given function in terms of D the elevation of the car above sea
level can be determined.
Responses:
- The slope is the decrease in the elevation per unit increase in distance from the top of the hill.
- The y-intercept is the elevation of the top of the hill above sea level.
- The x-intercept is the distance from the top of the hill top when the elevation of the car is at sea level.
How can the linear function for the slope and intercept be interpreted?
Given:
The function that gives the elevation of the car above sea level, from the top of the hill is given as follows;
Elevation above sea level = 7500 - 250·D
Where;
0 ≤ D ≤ 6
Required:
The meaning of the slope and intercepts of the graph of the function.
Solution:
From the given linear function, of the elevation of the car, we have;
- The slope which is -250 = The decrease in the elevation when the distance of the car from the top of the hill increases by 1 mile.
- The y-intercept, which is 7,500, is the elevation above sea level when the car is 0 mile from the top of the hill, which is when the car is at the top of the hill.
- The x-intercept is the point at which the elevation, which is the distance the car will be from the top of the hill when it is at sea level.
Learn more about linear functions here:
https://brainly.com/question/4025726