Understanding Linear Relationships and Rates

This lesson revisits constant rates, focusing on writing and graphing linear equations. Students learn key terms like constant rate, proportion, and linear equation. Through exercises, they apply these concepts to real-world problems, such as painting, walking, typing, and building birdhouses. The lesson emphasizes using proportions to derive equations and comparing slopes to determine speed. Students are encouraged to practice independently and complete an exit ticket.

What is the main focus of Lesson 22 in Module 4?

• Learning about geometric shapes

• Studying probability and statistics

• Exploring quadratic equations

• Understanding constant rates and graphing

Which term describes the speed at which something is done consistently?

• Fluctuating rate

• Constant rate

• Variable rate

• Proportional rate

How is a constant rate related to a linear equation?

• It is the y-intercept

• It is the slope

• It is the x-intercept

• It is the variable

In Exercise 1, what is the linear equation derived from Peter's painting rate?

• y = 2x + 1

• y = 3x

• y = 2x

• y = x + 2

What method is used to find the total area Peter paints after a given time?

• Using a calculator

• Using a table

• Using a graph or equation

• Using a ruler

In Exercise 2, how do you determine who walks faster between Nathan and Nicole?

• By comparing their heights

• By comparing their ages

• By comparing their weights

• By comparing their slopes

What is the slope of Nicole's walking equation?

• 2

• 5

• 4

• 3.57

In Exercise 3, who types faster, Susan or Ann?

• They type at the same speed

• Susan

• Ann

• Not enough information

In Exercise 4, how is Phil's birdhouse building rate represented?

• y = 2x

• y = 3/5x

• y = 5x

• y = x + 3

What is the general strategy for comparing proportional relationships?

• Comparing the variables

• Comparing the y-intercepts

• Comparing the slopes

• Comparing the x-intercepts