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): Write an equation to represent this data. Use calories as the y-coordinate and hours as the x-coordinate. Part 2 (2 points): What is the slope of the equation found in part 1? What does the slope represent in terms of the information provided? 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:
Create a table to find the two point require to make a line.
\[\begin{array}{|c|c|}
\hline
hours & calories \\ \hline
x & y\\ \hline
2 & 120 \\\hline
4 & 240 \\ \hline
\end{array}\]
Slope is defined as the change in x over the change in y or:
\(\Large{\frac{\triangle x}{\triangle y} = \frac{x_2-x_1}{y_2-y_1} = \frac{4-2}{240-120} = \frac{2}{120} = \frac{1}{60} =} \) Slope.
Use the point-slope formula to find the equation of the line.
\(y – y1 = m(x – x1)\) and plug in your values for x and y and (slope or m).
\(y-120 = \frac{1}{60}(x-2)\) Solve for y if required by your teacher.

Part 2: What does the slope mean? For every 1 hour of sleep, how many calories are burned?
Part3: How many calories burned after 8 hours? Plug in the number and solve the equation.