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Free Fall 2026 NC Math 1 Weekly Support

Week 2

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Tuesday

Tuesday - Learn & Practice: Writing Linear Expressions

I can translate real-world descriptions into linear expressions and function rules.

Short Lesson

Starting Value Plus Rate

A linear relationship often has the form y=mx+b, where m represents the rate of change and b represents the starting value.

Guided Examples

Build the Rule From the Story

Example 1

A plumber charges a $50 service fee plus $75 per hour.

Write a rule for the total cost C after h hours.

Step-by-step solution:

  1. Starting value: 50 The service fee is paid once.
Example 2

A video game account starts with 200 points and earns 15 points per level.

Write a rule for total points P after L levels.

Step-by-step solution:

  1. Starting value: 200 The account starts with 200 points.

Tuesday Practice

Write Each Rule

Use the starting value and rate of change. Keep editing your answer as you learn from feedback.

Problem 1

A service charges a $10 fee plus $2 per item. Write an expression for the total cost if n items are purchased.

Problem 2

You begin with 500 miles remaining on a trip and travel 60 miles each hour. Write a rule for the distance D remaining after h hours.

Problem 3

A subscription costs $15 to begin plus $5 per month. Write a rule for the total cost C after m months.

Problem 4

A tank starts with 20 gallons of water and drains at 2 gallons per minute. Write a rule for the amount of water V after m minutes.

Problem 5

You begin with $100 in savings and add $20 each week. Write a rule for the amount saved S after w weeks.

Problem 6

Concert tickets cost $50 per person, and parking costs a single $5 fee. Write a rule for the total cost C for p people.

Tuesday Reflection

What helps determine whether the rate of change should be positive or negative?

End of Tuesday

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