Assume a 125 pound person burns 150 calories after 15 minutes of jogging and 200 calories after 20 minutes of jogging.
Part 1: Write an equation to represent this data. Use calories as the y-coordinate and minutes as the x-coordinate.
Part 2: What is the slope of the equation found in part 1? What does the slope represent in terms of the information provided?
Part 3: How many calories will this person burn after 35 minutes of jogging? Using complete sentences, explain how the equation, slope, or graph can help to predict calories burned.
i have the same question. :P
Part 1: To write an equation that represents this data, we can use the slope-intercept form of a linear equation, given by y = mx + b, where y is the dependent variable (calories burned), x is the independent variable (minutes of jogging), m is the slope, and b is the y-intercept.
Since we have two data points, (15, 150) and (20, 200), we can calculate the slope as follows:
slope = (change in y) / (change in x)
= (200 - 150) / (20 - 15)
= 50 / 5
= 10
Now, we have the slope as 10. The equation representing this data is:
calories = 10 * minutes + b
To determine the value of b, we can substitute one of the data points into the equation. Let's use (15, 150):
150 = 10 * 15 + b
150 = 150 + b
150 - 150 = b
b = 0
Therefore, the equation that represents this data is:
calories = 10 * minutes
Part 2: The slope of the equation found in part 1 is 10. In terms of the information provided, the slope represents the number of calories burned per minute of jogging. So, for every additional minute of jogging, 10 calories are burned.
Part 3: To calculate the number of calories burned after 35 minutes of jogging using the equation, we simply substitute 35 for minutes:
calories = 10 * 35
calories = 350
Therefore, this person would burn 350 calories after 35 minutes of jogging.
The equation, slope, and graph can help predict calories burned by providing a mathematical relationship between the minutes of jogging and the calories burned. The equation allows us to calculate the calories burned for any given number of minutes, while the slope tells us the rate of calories burned per minute. By observing the graph of this linear equation, we can visually track and estimate the calories burned at different durations of jogging.