Linear Functions: Write Equations & Solve Real-World Problems

1. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the equation that represents the total cost (C) as a function of miles driven (m).

• C = 50 + 0.50m

• C = 50 - 0.20m

• C = 0.20 + m

• C = 50 + 0.20m

2. If a graph shows a line passing through the points (2, 3) and (4, 7), write the equation of the line in slope-intercept form.

• y = 3x - 3

• y = x + 1

• y = -2x + 5

• y = 2x - 1

3. A store sells notebooks for $2 each and pens for $1 each. If a student buys a total of 10 items for $16, write an equation to represent the relationship between the number of notebooks (n) and pens (p).

• n + p = 8, 2n + p = 18

• n + p = 10, 2n + p = 14

• n + p = 12, 2n + p = 14

• n + p = 10, 2n + p = 16

4. The temperature in a city increases linearly from 60°F to 80°F over 4 hours. Write an equation to model the temperature (T) as a function of time (h).

• T(h) = 15h + 45

• T(h) = 10h + 50

• T(h) = 5h + 60

• T(h) = 2.5h + 70

5. A gardener plants flowers in a straight line. If he plants 5 flowers in 2 hours, how many flowers will he plant in 5 hours? Write an equation to represent this situation.

• 10 flowers

• 12 flowers

• 8 flowers

• 15 flowers

6. A taxi company charges a base fare of $3 plus $1.50 per mile. If a passenger pays $12, how many miles did they travel? Write and solve the equation.

• 4 miles

• 8 miles

• 10 miles

• 6 miles

7. A gym membership costs $30 to join and $20 per month. Write an equation for the total cost (C) after m months and find the cost after 6 months.

• $150

• $90

• $180

• $120

8. A delivery service charges $5 for the first mile and $2 for each additional mile. Write an equation for the total cost (C) based on the number of miles (m) driven and find the cost for 10 miles.

• $23

• $18

• $15

• $30

9. A line graph shows the number of books read by a student over several months. If the student reads 3 books in the first month and increases by 2 books each month, write an equation to represent the number of books read (b) after m months.

• b = 2m + 3

• b = 3m + 1

• b = m + 3

• b = 2m + 1

10. A factory produces 100 toys in the first hour and increases production by 20 toys each subsequent hour. Write an equation to model the total number of toys produced (T) after h hours and find the total after 5 hours.

• 180

• 200

• 150

• 160