Algebra

PLEASE HELP! I'm stuck on these questions and I could really need some help rn :,)
1. Determine if the relationship is a linear function. Then represent the relationship using words and a graph.

Miles Traveled, x: 0 | Gallons of Gas, y: 11.2
Miles Traveled, x: 17 | Gallons of Gas, y: 10.2
Miles Traveled, x: 34 | Gallons of Gas, y: 9.2
Miles Traveled, x: 51 | Gallons of Gas, y: 8.2

2. A taxi company charges passengers $2.00 for a ride, and an additional $0.50 for each mile traveled. The function rule 𝑐 = 0.50𝑚 + 2.00 describes the relationship between the number of miles m and the total cost of the ride C. If the taxi company will only go a maximum of 40 miles, what is a reasonable graph of the function rule?

3. Evaluate the function for x = 2 and x = 7, when f(x) = -4x + 61

4. Tell whether the sequence is arithmetic. If it is, identify the common difference. ( 1/2, 1/3, 1/6, 0 … )

5. Tell whether the sequence is arithmetic. If it is, identify the common difference. (-3, -7, -10, -14 …)

6. You have a cafeteria card worth $50. After you buy lunch on Monday its value is $46.75. After you buy lunch on Tuesday, its value is $43.50. Write a rule to represent the amount on money left on the card as an arithmetic sequence. What is the value of the card after you buy 12 lunches?

7. What is the seventh term of an arithmetic sequence represented by the rule A(n) = -9 + (n-1)(.5)?

8. New grass seeds grow rapidly. A grass seed has grown to 0.3 millimeters tall. Tomorrow it will be 0.9 millimeters tall, the next day it will be 1.5 millimeters tall, and on the next day it will be 2.1 millimeters tall. Write a rule to represent the height of the bean plant as an arithmetic sequence. How tall will the plant be in 15 days?

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  1. #1. Note that as x grows by 17, y decreases by 1
    Thus ∆y/∆x is constant, meaning the relationship is linear
    y = 11.2 - 1/17 x

    #2. graph it. It's just straight line
    #3. just plug in the two values for x
    #4,5. it's arithmetic if the difference between terms is constant
    #6. Note that the amount changes by -3.25 each day (see #1)
    #7.Just plug in n=7
    #8. see #1,6

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