Constructing Linear Functions: Defining Equations

This video tutorial explains how to define a linear function by constructing an equation. It introduces the concepts of initial value and rate of change, using a practical example of a hiker descending a mountain. The tutorial guides viewers through identifying patterns, forming equations, and using these equations to predict outcomes. The key formula y = mx + b is explained, where m is the rate of change and b is the initial value.

What are the two main components that define a linear relationship?

• Slope and intercept

• Input and output

• Time and distance

• Initial value and rate of change

In the example of Greg's descent, what is the initial value?

• 0 feet

• 1,000 feet

• 10,000 feet

• 9,000 feet

How much does Greg descend every hour?

• 1,500 feet

• 500 feet

• 1,000 feet

• 2,000 feet

What is the pattern used to determine Greg's position after a certain number of hours?

• Multiply hours by 1,000 and add 10,000

• Multiply hours by -1,000 and add 10,000

• Multiply hours by -1,000 and subtract 10,000

• Multiply hours by 1,000 and subtract 10,000

What does the 'm' represent in the equation y = mx + b?

• Rate of change

• Initial value

• Input

• Output

In the equation y = mx + b, what does 'b' stand for?

• Input

• Output

• Initial value

• Rate of change

How can the linear equation y = mx + b be used in practical scenarios?

• To calculate the speed of a car

• To solve quadratic equations

• To determine the area of a rectangle

• To predict future values based on a linear relationship