A mountain road is 5 miles long and gains elevation at a constant rate. After 2 miles, the elevation is 5500 feet above sea level. After 4 miles, the elevation is 6200 feet above sea level.
What would be the equation of this line?

Find the elevation of the road at the point where the road begins.


Describe where you would see the point in part (a) on a graph where represents the elevation in feet and represents the distance along the road in miles.

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Answer:

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Step-by-step explanation:

Ver imagen madisonstahl45

The elevation of the road 4800 feet at the beginning and it gains elevation at a constant rate of 350 feet per mile.

A linear equation is in the form:

y = mx + b;

where m is the rate of change, b is the initial value of y and y, x are variables.

Let y represent the elevation of the road after x miles.

After 2 miles, the elevation is 5500 feet above sea level. Hence:

5500 = 2m + b   (1)

After 4 miles, the elevation is 6200 feet above sea level. Hence:

6200 = 4m + b   (2)

Solving equation 1 and 2 simultaneously gives:

m = 350, b = 4800

The elevation of the road 4800 feet at the beginning and it gains elevation at a constant rate of 350 feet per mile.

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