Rate of Change and Linear Functions

The video tutorial explains how to find constants from a table by examining ratios and simplifying them. It introduces the concept of rate of change, calculated by the change in y over the change in x, and demonstrates how to apply this to equations. The tutorial also covers analyzing more complex tables with varying increments and provides practice problems for students to solve on their own.

What is the first step in finding the constant from a table?

• Multiply all x values by 2.

• Calculate the difference between x values.

• Examine the ratios of y over x.

• Look at the sum of all y values.

How do you determine the rate of change from a table?

• By adding all x values together.

• By dividing the change in y by the change in x.

• By subtracting the smallest y value from the largest.

• By multiplying the change in x by 2.

In the simple table example, what is the rate of change when x increases by 1?

• 3

• 4

• 6

• 5

What does the equation y = 6x imply when x = 1?

• y = 1

• y = 12

• y = 6

• y = 18

In the complex table, what is unusual about the x increments?

• They are all even numbers.

• They decrease by 1 each time.

• They remain constant.

• They vary and do not increase uniformly.

How is the rate of change calculated in the complex table when x increases by 3?

• By adding 3 to the change in y.

• By dividing the change in y by 3.

• By subtracting 3 from the change in y.

• By multiplying the change in y by 3.

What is the rate of change when y changes from 24 to 30 and x changes by 2?

• 4

• 1

• 2

• 3

What should students do to practice finding the rate of change?

• Draw a table and calculate the sum of x values.

• Write an essay on the importance of rate of change.

• Draw a table and find the rate of change using y and x values.

• Memorize the formula for rate of change.