While at Bryce Canyon National park, Jorge and Jackie went hiking on the Under t

Question

While at Bryce Canyon National park, Jorge and Jackie went hiking on the Under the Rim trail to Yellow Creek. The table shows their progress down to Yellow Creek.

Table shows their descent in time and elevation

Find the slope for the data in the table. Interpret the slope as a rate of change, including units.

I came up with a slope (m) = 1 over 2, 1 being vertical change and 2 being horizontal change. Is this correct?

This question also asks what the elevation was 18 minutes after Jorge and Jackie began. I can see that for every 10 minutes of descent, the elevation drops by 400 feet. I can calculate they would be at 7,020 feet at 18 minutes, but I do not know how to show this in algebra terms with respect to slope, etc.

The last part of the question asks when were they at 7000 feet elevation? I come up with 22.5, or 22 minutes and 30 seconds, but again, I do not know how to show this in algebra terms as required.

Thank you in advance for your help.

Explanation / Answer

slope : take any two sets of (time , elevation)

Lets take 1st two: slope = ( 7500 - 7900)/(10 - 0) = -400/10 = -40 ft/min

elevation after 18 minutes

Lets find a linear equation with the given slope:

y = mx + c ; y = -40x+ c ; c= 7900

y = -40x +7900

at x= 18 min. elevation, y = -40*18 + 7900 = 7180 feet

wheny elevation y = 7000 ft

So, 7000 = -40x + 7900

x = 900/40 = 90/4 = 22.5 min

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