Understanding Linear Functions

This video tutorial by Mr. Weaver covers eighth-grade module 5, lesson 3 on constructing linear functions. It explains how to write linear functions from graphs, tables, and verbal descriptions by identifying the rate of change and initial value. The lesson includes examples and exercises to practice constructing linear functions using different methods, emphasizing the importance of understanding the slope and y-intercept in forming equations.

What is the form of a linear function equation?

• y = a/x + b

• y = ax^2 + bx + c

• y = mx + b

• y = ax + b^2

In a linear function, what does the slope represent?

• The rate of change

• The y-intercept

• The initial value

• The x-intercept

How do you find the slope from a graph?

• By finding the midpoint of the line

• By calculating the ratio of rise over run

• By counting the number of grid squares

• By measuring the distance between two points

What is the initial value in a linear function?

• The x-coordinate when y is zero

• The y-coordinate when x is zero

• The midpoint of the line

• The slope of the line

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

• By subtracting the smallest x-value from the largest

• By adding all the y-values together

• By multiplying the x-values by the y-values

• By finding the difference in y-values divided by the difference in x-values

What is the initial value in a table of a linear function?

• The average of all y-values

• The y-value when x is zero

• The last y-value

• The first y-value

In a verbal description, what word often indicates the rate of change?

• Total

• Per

• Difference

• Sum

How do you find the initial value from a verbal description?

• By subtracting the rate of change from the total

• By calculating the average rate of change

• By identifying the starting point when x is zero

• By finding the midpoint of the data

What is the equation form for a linear function?

• y = mx + b

• y = ax^2 + bx + c

• y = a/x + b

• y = ax + b^2

What is the significance of the y-intercept in a linear function?

• It represents the slope of the line

• It is the point where the line crosses the y-axis

• It is the highest point on the line

• It is the average of all y-values