Gps Hiking Devices

Simple slope word problem?

Daniela and Jack are hiking a steady incline. They use their GPS device to determine their elevation every 15 minutes. At 15 minutes and 30 minutes they were at elevations of 10,300 feet and 10,900 feet, respectively.

a. Write an equation expressing their elevation in relation to time.
b. Based on the formula, what is their elevation after 1 hour?

The equation for slope is rise/run

In this case, our x axis is time, and the y axis is elevation.

so we have the two points (15, 10300) and (30,10900)

rise/run = (y2-y1)/(x2-x1) = (10900-10300)/(30-15) = (600)/(15) = 40.

Therefore the slope of this line is 40.

The general equation for a line is y = mx + b. where m is the slope, and b is the y-intercept

y = 40x + b. We know that when x is 15, y is 10300. Substituting these values into the equation, we can solve for b.

10300 = 40(15) + b
10300 = 600 + b
10300 – 600 = b
b = 9700

So our equation for the elevation in relation to time is
y = 40x + 9700

We can check this with the values we were given
10300 = 40*(15) + 9700
10900 = 40*(30) + 9700

To calculate after one hour, first we must realize that our formula is in terms of elevation per minute. We must convert 1 hour into minutes

1 hour = 60 minutes

our equation is then:

y = 40*(60) + 9700
y = 12100

Therefore, after one hour, their elevation is 12100 feet.

Hope this helps
Cheers

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