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.

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.

slicergiza slicergiza · Answer 2 · 2020-01-02T05:32:03+01:00

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.