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Equation for calories burned

# 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

 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