Proportional Relationships and Linear Equations

This lesson, led by Mrs. Apia, explores proportional relationships involving average and constant speed to derive linear equations in two variables. Students learn to solve problems related to distance and time, using examples like Paul's walking and Stephanie's driving. The lesson emphasizes the importance of understanding unit rates and proportions to form linear equations, providing exercises to reinforce these concepts.

What is the main focus of the lesson introduced by Mrs. Apia?

• Understanding quadratic equations

• Exploring proportional relationships and linear equations

• Learning about geometric shapes

• Studying historical events

If Paul walks 2 miles in 25 minutes, how far can he walk in 50 minutes?

• 3 miles

• 4 miles

• 6 miles

• 5 miles

What is the linear equation form used to relate distance and time?

• y = mx + b

• y = kx

• y = x^2

• y = x + c

How is the unit rate defined in a proportional relationship?

• Y minus X

• X divided by Y

• Y divided by X

• X multiplied by Y

In the example problem, what is the unit rate for 123 miles in 3 hours?

• 43 miles per hour

• 42 miles per hour

• 40 miles per hour

• 41 miles per hour

What fraction represents Wesley's constant speed if he walks 1.5 miles in 25 minutes?

• 1.5/35

• 1.5/20

• 1.5/25

• 1.5/30

How many miles does Wesley walk in 15 minutes at his constant speed?

• 0.5 miles

• 1.1 miles

• 0.7 miles

• 0.9 miles

What is the linear equation for Stephanie's drive if she travels 20 miles in 45 minutes?

• y = 7/9 x

• y = 6/9 x

• y = 5/9 x

• y = 4/9 x

How long does it take Stephanie to reach halfway to her friend's house?

• 20 minutes

• 27.5 minutes

• 22.5 minutes

• 25 minutes

What is the purpose of writing a linear equation in two variables in this lesson?

• To find the perimeter

• To calculate area

• To relate distance and time

• To solve quadratic equations