Understanding Linear Functions

The video tutorial explains how to determine the value of a linear function at a specific point using a given table. It covers the concept of linear functions, focusing on the constant rate of change represented by the slope (m) and the vertical intercept (b). The tutorial demonstrates how to calculate the slope by examining changes in Y and X values and how to derive the function rule f(x) = mx + b. Finally, it evaluates the function at x = 3, showing the step-by-step calculation to find the result.

What is the formula for a linear function?

• f(x) = ax^2 + bx + c

• f(x) = mx + b

• f(x) = a/x + b

• f(x) = x^2 + 2x + 1

How is the slope of a linear function determined?

• By adding the change in y to the change in x

• By multiplying the change in y by the change in x

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

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

If y increases by 8 when x increases by 2, what is the slope?

• 8

• 16

• 4

• 2

What is the vertical intercept (b) if the ordered pair is (0, -3)?

• -3

• 0

• 3

• 1

What is the value of f(3) for the function f(x) = 4x - 3?

• 3

• 9

• 12

• 15