Question

Keon and Lesha are comparing their daily calorie intake. Each day, Lesha chooses healthy 100-calories snacks such as apples and carrots while Keon chooses snacks like chips and candy that have 200 calories each.

Answer 1

Scale for the horizontal axis is in increments of 1. Scale for the vertical axis in in increments of 100. Black – Lesha, Blue - Keon Part B:What does the rate of change for each line represent? The rate of change represents the amount of calories per snack.Part C:What is Lesha’s rate of change? Answers will vary.Example: 100 calories/snack. Part D:How does Lesha’s rate of change compare to Keon’s rate of change? Why are the two rates different from one another? In this case it doubles - the rates are different because with healthy snacks the caloric intake per snack is less than unhealthy snacks.

Answer 2

Answer:

Let x represents the number of snacks and y represents the calories from x snacks.

Here,

Calories taken by Lesha for 1 snack = 100,

So, total calories taken by him/her for x snacks,

y = 100x  .................(1),

Similarly, Calories taken by Keon for 1 snack = 200,

So, total calories taken by him/her for x snacks,

y = 200x  .................(2),

Equation (1) and (2) are lines. ( ∵ they are in the form of y = mx + c ),

Part A : Graphing :

In eq (1),

if x = 1, y = 100,

if x = 0, y = 0.

if x = 2, y = 200,

Join points (1, 100), (0,0) and (2, 200), we get the graph of line y = 100x,

Note : We don't take negative value of x because number of snakes must be greater or equal to 0.

Similarly, In eq (2),

if x = 1, y = 200,

if x = 0, y = 0.

if x = 2, y = 400,

Join points (1, 200), (0,0) and (2, 400), we get the graph of line y = 200x,

Part B :

For a line y = mx + c, m represents rate of change,

By comparing,

Rate of change for line (1) = 100,

Rate of change for line (2) = 200,

i.e. rate of change represents the calories per unit snacks.

Part C :

Lasa rate of change = Rate of change for line (1) = 100 calories per snack.

Part D :

∵ 100 < 200

That is, Lesha's rate of change is less than that of Keon.

The rates are different because they are eating different snacks.