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The information that Lashawn and Isaac have collected has come from different sources. It is given in a variety of formats. Review the route descriptions on the Driving Routes Cards, and answer the following questions.

What are the starting values for each driving route? Give each as an ordered pair and as a sentence in context.

Driving Route A:

Driving Route B:

Driving Route C:

Driving Route D:

What is the rate of change for each driving route? Give each as a unit rate and as a sentence in context.

Driving Route A:

Driving Route B:

Driving Route C:

Driving Route D:

Review the routes on the Driving Routes Cards and the information in question 1.

Graph each driving route below. Label each line with A, B, C or D. Identify the x- and y-intercepts by writing the ordered pair near each point.

Which driving route will get Lashawn and Isaac to their destination the fastest? How long will it take?

Driving routes A, D, and B all have the same y-intercept. Why do they have different arrival times?

1 answer

To assist you with your requests regarding the driving routes, I'll need to establish hypothetical values for each driving route as from the details provided above are missing. Let's assume the following starting points and rates of change for each route:

** Driving Route A: **

  • Starting Value: (0, 0)
  • Context Sentence: The starting point for Driving Route A is (0, 0), which represents the origin of their journey.

** Driving Route B: **

  • Starting Value: (0, 5)
  • Context Sentence: Driving Route B begins at the point (0, 5), indicating that it starts 5 miles from the origin.

** Driving Route C: **

  • Starting Value: (0, 10)
  • Context Sentence: The starting point for Driving Route C is (0, 10), meaning it starts 10 miles from the origin.

** Driving Route D: **

  • Starting Value: (0, 4)
  • Context Sentence: Driving Route D has its starting point at (0, 4), which is 4 miles from the origin.

Rate of Change for Each Driving Route

Driving Route A:

  • Rate of Change: 60 miles/hour
  • Context Sentence: Driving Route A travels at a rate of 60 miles per hour.

Driving Route B:

  • Rate of Change: 50 miles/hour
  • Context Sentence: The rate of change for Driving Route B is 50 miles per hour.

Driving Route C:

  • Rate of Change: 40 miles/hour
  • Context Sentence: Driving Route C has a rate of change of 40 miles per hour.

Driving Route D:

  • Rate of Change: 70 miles/hour
  • Context Sentence: Driving Route D operates at a rate of 70 miles per hour.

Graph of Each Driving Route

Here are hypothetical equations based on the assumed starting points and rates of change:

  • Drive Route A: y = 60x (A)
  • Drive Route B: y = 50x + 5 (B)
  • Drive Route C: y = 40x + 10 (C)
  • Drive Route D: y = 70x + 4 (D)

You would graph these lines on a coordinate plane and label the lines (A, B, C, D), marking the x- and y-intercepts accordingly, which for these equations would be:

  • Route A: (0,0) and (1,60)
  • Route B: (0,5) and (1,55)
  • Route C: (0,10) and (1,50)
  • Route D: (0,4) and (1,74)

Fastest Route and Time

Based on the rates provided, Driving Route D would get Lashawn and Isaac to their destination the fastest, traveling at 70 miles/hour. The time it takes would depend on the total distance they need to cover; if this were 100 miles, for example:

Time = Distance / Rate = 100 miles / 70 miles/hour ≈ 1.43 hours (or about 1 hour and 26 minutes).

Why Different Arrival Times Despite Same Y-Intercept

Driving routes A, D, and B have different arrival times despite sharing the same y-intercept (origin) because their rates of change differ. The y-intercept represents the initial starting distance, but the slope indicates the speed at which each route travels. Therefore, the route with a higher rate of change will arrive faster even if they start from the same point on the y-axis.

If you provide the actual details of the driving routes mentioned, I can tailor the information accordingly.