Linear Equations and Constant Rates

The video tutorial covers the concept of constant rate, using examples like lawn mowing, water flow, typing speed, painting rate, and walking speed. It explains how to set up proportions, solve for unknowns using cross-multiplication, and derive linear equations. The tutorial also includes exercises for practice and demonstrates graphing results to visualize relationships.

If Paulie mows 35 square feet in 2.5 minutes, how much can she mow in 10 minutes?

• 150 square feet

• 120 square feet

• 140 square feet

• 130 square feet

What is the linear equation derived from the mowing example?

• y = T/35

• y = 2.5/35 * T

• y = 35 * T

• y = 35/2.5 * T

In the water flow example, what is the constant rate of water flow in gallons per minute?

• 2.5 gallons/min

• 5.5 gallons/min

• 4.5 gallons/min

• 3.5 gallons/min

How many pages can Juan type in 10 minutes if he types at a constant rate of 1 page in 3.5 minutes?

• 3.5 pages

• 2.9 pages

• 2.5 pages

• 3.0 pages

How long would it take Juan to type a 5-page paper?

• 17.5 minutes

• 15 minutes

• 18.5 minutes

• 20 minutes

What is the linear equation for Emily's painting speed if she paints 32 square feet in 5 minutes?

• a = 32 * T

• a = 32/5 * T

• a = 5/32 * T

• a = T/32

If Emily paints at a constant rate, how many square feet can she paint in 2.5 minutes?

• 14 square feet

• 16 square feet

• 20 square feet

• 18 square feet

What is the constant rate of Joseph's walking speed if he walks 0.5 miles in 6 minutes?

• 0.083 miles/min

• 0.1 miles/min

• 0.09 miles/min

• 0.075 miles/min

How long would it take Joseph to walk 4 miles at his constant speed?

• 42 minutes

• 50 minutes

• 45 minutes

• 48 minutes

What is the purpose of using a linear equation in these examples?

• To predict values for different times

• To calculate the exact time taken

• To find the maximum rate

• To determine the minimum rate