Point-Slope Equations and Slope Calculation Challenge

1. A car rental company charges a flat fee of $50 plus $20 for each day the car is rented. Write the point-slope equation for the total cost (C) based on the number of days (d) rented, using the point (1, 70).

• C - 70 = 20(d - 1)

• C - 50 = 20(d - 1)

• C = 20d + 30

• C - 70 = 15(d - 1)

2. A gardener is planting a row of trees. The first tree is planted at the point (2, 5) and the second tree at (4, 9). What is the slope of the line that connects these two trees?

• 4

• 3

• 2

• 1

3. A bike shop sells bikes for $300 each. If a customer buys 3 bikes, the total cost is $900. Write the point-slope equation for the total cost (C) based on the number of bikes (b) purchased, using the point (3, 900).

• C - 900 = 200(b - 3)

• C = 300b + 300

• C - 900 = 400(b - 3)

• C - 900 = 300(b - 3)

4. A student scored 75 on their first test and 85 on their second test. What is the slope of the line that represents the student's test scores over time?

• 15

• 5

• 20

• 10

5. A delivery service charges $10 for the first mile and $2 for each additional mile. Write the point-slope equation for the total charge (C) based on the number of miles (m) driven, using the point (1, 12).

• C - 12 = 10(m - 1)

• C = 2m + 10

• C - 10 = 2(m - 1)

• C - 12 = 2(m - 1)

6. A restaurant's bill for a meal is $40 for 2 people. If the cost increases to $60 for 4 people, what is the slope of the line representing the cost per person?

• -5

• 0

• 1.5

• -2.5

7. A phone plan costs $30 per month plus $0.10 per text message. Write the point-slope equation for the total cost (C) based on the number of text messages (t) sent, using the point (0, 30).

• C - 30 = 0.05(t - 0)

• C = 0.10t - 30

• C - 30 = 0.10(t + 1)

• C - 30 = 0.10(t - 0) or C = 0.10t + 30

8. A train travels from station A to station B, covering 100 miles in 2 hours. What is the slope of the line representing the train's speed?

• 25 miles per hour

• 100 miles per hour

• 75 miles per hour

• 50 miles per hour

9. A bookstore sells novels for $15 each. If a customer buys 5 novels for $75, write the point-slope equation for the total cost (C) based on the number of novels (n) purchased, using the point (5, 75).

• C = 15n + 5

• C - 75 = 10(n - 5)

• C - 75 = 15(n - 5)

• C - 75 = 20(n - 5)

10. A swimming pool is filled with water at a rate of 10 gallons per hour. If the pool has 50 gallons of water after 5 hours, what is the slope of the line representing the water level over time?

• 10 gallons per hour

• 20 gallons per hour

• 15 gallons per hour

• 5 gallons per hour