Question

Assume a 150 pound person burns 120 calories after 2 hours of sleep and 240 calories after 4 hours of sleep.
Part 1 (2 points): Use calories as the y-coordinate and hours as the x-coordinate. After writing two ordered pairs, find the slope. What does the slope represent in terms of the information provided?

Part 2 (2 points): Write an equation, in slope intercept form, to represent this data.

Part 3 (2 points): How many calories will this person burn after 8 hours of sleep? Using complete sentences, explain how the equation, slope, or graph can help to predict calories burned.#

Answer 1

Part 1. Two ordered pairs, or points, that were given are (x1,y1) = (2, 120) and
(x2,y2) = (4,240). The slope is given by the change in y divided by the change in x, or
(y2 - y1)/(x2 - x1) . Substitute the information for the points you were given:
(240 - 120)/(4 - 2) = 120/2 = 60 In this problem, since the y represents calories burned and the x represents hours of sleep, the slope represents the number of calories burned per hour of sleep.

Part 2. Your slope, m, is 60. The slope-intercept equation of a line is y = mx + b, where m is the slope and b is the y-intercept (the value of y when x is 0). To figure out what b is, we can use one of the (x,y) pairs we were given. For example, we could use (2, 120):

y = mx + b --> 120 = 60(2) + b --> 120 = 120 + b --> b = 0 This means that when you sleep 0 hours, the amount of calories you burn is also 0. So, the equation of the line is
y = 60x + 0 , or just y = 60x

Part 3. Since y = 60x, when x = 8 hours, y = (60 calories/hr.)(8 hours) = 480 calories
To use the equation to find the number of calories burned, plug in the desired number of hours for x. Then 60 times the number of hours you plugged in will tell you how many calories you burned. Or, you could also graph the line, then find the point on the line that corresponds with the x value (number of hours) you want to know. The y coordinate of the point will give the number of calories burned.