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Equation for calories burned
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Equation for calories burned








































According to the American Heart Association, the number of calories a 100 pound person burns when bicycling 12 miles per hour is 270 calories per hour. A 150 pound person burns 410 calories per hour when bicycling 12 miles per hour.

1. Write a linear equation which shows the relationship between weight and calories burned per hour.

2. Use the linear equation to prepare an x-y table.

3. If a person weighs 175 pounds, how many calories per hour would they burn?

4. If a person weighs 90 pounds, how many calories per hour would they burn?

Comments for Equation for calories burned

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Jun 27, 2012
Equation for calories burned
by: Staff


The answer:

1. Write a linear equation which shows the relationship between weight and calories burned per hour.

y = calories burned per hour

x = weight in pounds


the standard slope intercept form of a linear equation is:

y = mx + b


compute the slope “m” using the two data points given in the problem


A 100 pound person burns when bicycling 12 miles per hour is 270 calories per hour

(x₁,y₁)

x₁ = 100 pounds
y₁ = 270 calories per hour

(x₁,y₁) = (100, 270)


A 150 pound person burns 410 calories per hour when bicycling 12 miles per hour

(x₂,y₂)

x₂ = 150 pounds
y₂ = 410 calories per hour

(x₂,y₂) = (150, 410)


Slope “m” = (y₂ - y₁) / (x₂ - x₁)

m = (410 - 270) / (150 - 100)

m = (140) / (50)

m = 2.8


y = mx + b

y = 2.8x + b

compute the “y intercept” using the values for either known point: (100, 270) or (150, 410)

using the first point (100, 270)

y₁ = 2.8x₁ + b

270 = 2.8 * 100 + b

270 = 280 + b

280 - 280 + b = 270 - 280

0 + b = 270 - 280

b = 270 - 280

b = -10


>>> the final equation is: y = 2.8x - 10

(calories burned per hour) = (2.8) * (weight in pounds) - 10



2. Use the linear equation to prepare an x-y table.

x, y = 2.8x - 10

100, 2.8*100 - 10 = 270

110, 2.8*110 - 10 = 298

120, 2.8*120 - 10 = 326

130, 2.8*130 - 10 = 354

140, 2.8*140 - 10 = 382

150, 2.8*150 - 10 = 410




x, y

100, 270

110, 298

120, 326

130, 354

140, 382

150, 410



3. If a person weighs 175 pounds, how many calories per hour would they burn?

(calories burned per hour) = (2.8) * (weight in pounds) - 10

(calories burned per hour) = (2.8) * (175 pounds) - 10

>>> calories burned per hour = 480



4. If a person weighs 90 pounds, how many calories per hour would they burn?


(calories burned per hour) = (2.8) * (weight in pounds) - 10

(calories burned per hour) = (2.8) * (90 pounds) - 10

>>> calories burned per hour = 242



Thanks for writing.

Staff
www.solving-math-problems.com


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