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Free Fall 2026 NC Math 1 Weekly Support

Week 4

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Tuesday

Tuesday - Applications of Linear Functions

I can interpret rate of change and starting values in context.

Why It Matters

Linear Models Describe Changing Quantities

Linear models help us describe and predict situations involving cost, distance, growth, savings, and other changing quantities.

Rate of Change

The slope m tells how much the output changes for every 1 unit of input.

Starting Value

The value b tells what happens when x=0.

Reasonable Values

Domain and range should make sense in the real-world situation.

Guided Examples

Interpret the Numbers in Context

Example 1

A tank starts with 50 gallons of water and loses 2 gallons each hour.

Write and interpret a linear model.

Step-by-step solution:

  1. x=hours, y=gallons remaining Identify the variables.
Example 2

A bike rental costs $10 plus $5 per hour.

Interpret the rate, starting value, and domain.

Step-by-step solution:

  1. y=5x+10 Identify the model.

Tuesday Practice

Say What the Model Means

Keep the context attached to your answer. Units matter.

Problem 1

A phone plan costs a $30 base fee plus $5 per gigabyte. What does the 5 represent?

Example format: $5 per gigabyte

Problem 2

You start with $100 in savings and add $20 each week. Write a linear model.

Example format: y=20x+100

Problem 3

A plant is modeled by h=2t+10, where t is time in weeks and h is height in centimeters. What does 10 represent?

Example format: starting height of 10 centimeters

Problem 4

A ticket situation is modeled by y=15x+5, where x represents the number of tickets purchased. Why must the domain use nonnegative values?

Choose one

Problem 5

If y=50 and y=2x+10, find x.

Example format: 20 or x=20

Tuesday Reflection

Which strategy helped you interpret a linear model?

End of Tuesday

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