Constructing Linear Functions from Graphs

The video tutorial explains linear functions, their representations, and how to convert a graph into a linear equation. It covers the components of the linear equation y = mx + b, focusing on the slope (m) and y-intercept (b). Two examples demonstrate finding linear equations from graphs, one with a positive slope and another with a negative slope. The tutorial also includes a method to verify the correctness of the derived equations.

Which of the following is NOT a characteristic of a linear function?

• It shows a constant change in y as x increases by 1.

• It has exponents larger than 1.

• It can be written as y = mx + b.

• It forms a straight line on a graph.

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

• The x-intercept

• The rate of change

• The slope of the line

• The y-intercept

How do you determine the slope 'm' from a graph?

• By measuring the distance between two points

• By finding the y-intercept

• By calculating rise over run

• By identifying the x-intercept

In the example where the y-intercept is 3, what is the slope of the line?

• 3

• 1/3

• -3

• -1/3

What is the equation of the line if the slope is -4 and the y-intercept is 2?

• y = 4x + 2

• y = 2x - 4

• y = -4x + 2

• y = -2x + 4