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Math 1 Summer Bridge

Day 2: Linear Relationships

Connect slope, rate of change, y-intercept, tables, graphs, and equations.

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Student Goal

I can identify and describe a linear relationship using a table, graph, equation, or situation.

Why It Matters

Linear relationships are one of the biggest ideas in Math 1. They appear in rates, graphing, functions, modeling, and systems.

Warm-Up

Warm-Up 1

In y = 3x + 4, what is the slope?

Warm-Up 2

A table has y-values 2, 5, 8, 11 as x increases by 1. What is the rate of change?

Short Lesson

Standard Focus

NC.M1.F-LE.1 and NC.M1.F-LE.2: Linear functions and constant rate of change

Student-Friendly Standard Goal

I can recognize a constant rate of change and write or interpret a linear equation.

  • A linear relationship has a constant rate of change.
  • Slope tells how much y changes when x increases by 1.
  • The y-intercept is the starting value when x = 0.
  • Slope-intercept form is y = mx + b, where m is slope and b is the y-intercept.

Guided Examples

Guided Example 1

Find the Equation from a Table

Use the table to write a linear equation.

Step 1

5, 7, 9, 11

What is the rate of change?

Guided Example 2

Interpret a Linear Situation

A gym charges 20 to join and 8 per month. Write the model.

Step 1

C = ?m + ?

Which number is the rate of change?

Practice

Problem 1

What is the y-intercept of y = -2x + 9?

Problem 2

A line has slope 4 and y-intercept 1. Write the equation.

Problem 3

Which table looks linear?

Problem 4

Choose the next step: To graph y = 2x - 3, start at...

Problem 5

True or false: A linear relationship must have a constant rate of change.

Reflection

How are you feeling about today's skill?

Optional reflection: What is one step, word, or representation from today that you want to remember when Math 1 starts?