Understanding Linear Functions

The video tutorial explains how to identify and write function rules for linear functions using tables of data. It covers calculating the slope and y-intercept, and provides three examples of increasing complexity to illustrate the process. The tutorial emphasizes understanding the relationship between changes in x and y values to determine the linear function's equation.

What type of function is identified when there is a constant change in y for every constant change in x?

• Quadratic function

• Exponential function

• Linear function

• Logarithmic function

What is the formula used to represent a linear function?

• y = log(x)

• y = ax^2 + bx + c

• y = mx + b

• y = a^x

How do you calculate the slope of a linear function?

• Change in y over change in x

• Product of x and y

• Sum of x and y

• Change in x over change in y

If the slope of a line is 3, what does this indicate about the change in y when x increases by 1?

• y decreases by 3

• y increases by 3

• y increases by 1

• y remains constant

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

• The x-intercept

• The slope of the line

• The rate of change

• The y-intercept

What is the y-intercept of the function y = 2x + 5?

• 2

• 5

• 0

• 7

In the advanced example, what is the slope of the function derived from the points given?

• 5

• 3

• 7

• 2

What is the y-intercept of the function derived from the advanced example?

• 7

• -5

• 0

• 5

If a function has a slope of 7, what is the change in y when x increases by 2?

• 2

• 9

• 14

• 7

What is the main takeaway from learning how to derive a function rule from a table of values?

• Identifying exponential growth

• Deriving linear function rules

• Understanding quadratic functions

• Calculating logarithmic values