Complete your Week 2 discussion prompt:
A Linear Equation is a rule that assigns to each number x on the x-axis exactly one number y on the y – axis so that the ordered pairs (x,y) form a line. We call y the Dependent Variable and we call x the Independent Variable because the value assigned to y by the linear equation will depend on the value selected for x.
Now consider this scenario: we can burn 4 calories by walking 100 steps. The linear equation modeling this scenario is C=0.04*S where C is the dependent variable and S is the independent variable. Here, C represents calories burned for some number of steps S walked. Use this calorie burning model for walking to answer the following questions:
1) How many calories have been burned after a step count of 600 steps??
2) How many steps does it take to burn 500 calories in one day?
Next, you will create a new linear model that shows the amount of calories burned in a given day during some activity you choose, compensating for food intake. Produce a model with a reasonable rate of calorie burn for walking, running, or some other activity (provide the source of your rate), and account for a daily calorie intake between 1200 and 3000 calories. Be sure to describe the detailed scenario for which your equation models. Conclude your post by rewording the following questions to fit your scenario:
1) How many calories have been burned after 1 typical session of activity?
2)How much activity does it take to burn all the calories eaten in one day?
Substantive Participation Guideline: When responding to a peer’s linear scenario and problem, set up the linear equation (formula) that describes the scenario and answer the two parts of the scenario. Demonstrate and explain your thinking to support your answers.
Students,
This week we will model (come up with a formula!) a real-life scenario that has the pattern of a linear relationship (straight-line). A linear relationship occurs when two quantities are related with each other in the following manner: as one quantity increases, the other quantity also increases at the same (constant) change of rate (always multiplied by the same amount). When you make a picture (a graph) of these two quantities, you will see a straight line going up from left to right, such as the one below. The graph below is describing the pattern “The more time you are driving, more distance you will travel.” From the graph, every hour driving is the equivalent of 25 miles traveled, so the constant change of rate here is 25.
linear.rel.png
Similarly occurs when two quantities are related with each other in the following manner: as one quantity decreases, the other quantity also decreases at the same change of rate (multiplied by same amount). When you make a picture (a graph) of these two quantities , you will see a straight line going down from left to right, such as the one below. The graph below is describing the pattern “The more time we wait to fix the broken pipe, more gallons of water are lost.” From the graph, every hour we wait is the equivalent of 5 gallons of water lost, so the constant change of rate here is -5.
linear.rel.2.png
We can set up a formula (or equation) to describe linear patterns. A linear relationship between two quantities has two parts: (a) The initial value (also known as b) and (b) a constant rate of change (also known as m). Linear relationships are written as the following formula or equation y = mx + b.
One real-life example is the amount of money you earn working by the hour. For example, sales people have a weekly base salary and earn a commission depending how many items they can sell in a week. Let’s say a sales person has a base salary of $200 and earns $5 for every item they sell. In this case, $200 is the initial value (b) and $5 per item is the constant rate of change (m). If let variable y to be the amount of money the sales person earns in the week and the variable x to be the number of items the sales person sold, then the equation will be y = 5x + 200.
The formula or equation y = 5x + 200 can be used as a formula to calculate how much money a sales person could earn if they sell a certain number of items. If the person sells 20 items, this person will earn $300 because if we plug in x with 20, we get y = 5(20) + 200.
Does this help?
Respond to (2) peers:
Peer (1) kristine:
Hello Class,
Ok, hope I did this correctly!!
1) After a step count of 600 steps, 24 calories have been burned.
2) It takes 12500 steps to burn 500 calories.
Professor Diaz burns 300 calories per hour on his daily bike route. On a typical day, his bike route takes him 1 1/2 hours to completes. Ever since he started his daily bike routes, he maintains his daily calorie intake eaten to 1800.
1)After a typical 1 1/2 hour bike route, how many calories does he burn?
2) Based on his daily 1800 calorie intake, how many times must he complete his bike route to burn the total calories eaten in one day?
Peer (2) Diana
Hi, here is my revised post:
Your linear equation is C=0.04*S where C is the dependent variable and S is the independent variable.
1. There are 24 calories burned after 600 steps since S=0.04*600 = 24
2. It would take 12,500 steps to burn 500 calories in one day since 500 / 0.04 = 12,500.
My activity is swimming and I burn 20 calories per minute. At the gym, I swam for 30 minutes. In a typical day, I eat 2,000 calories.
1) If I swim for 30 minutes, how many calories did I burn?
2) Based on my daily 2,000 calorie intake, how long does the swim need to be to burn the total calories eaten in one day?
Reply to initial post and both peers
