Connecting Graphs, Equations, and Tables in Linear Relationships

The video tutorial explains how to convert graphs of linear relationships into equations and tables. It begins with an introduction to linear relationships, highlighting the importance of the y-intercept and rate of change. The tutorial then demonstrates how to create a table of ordered pairs from a graph to determine these key features. Several examples are provided, each illustrating different scenarios such as positive, fractional, and negative rates of change. The video concludes with the derivation of equations in the form y = mx + b for each example.

What is the general form of a linear relationship?

• y = cx + b

• y = bx + m

• y = mx + b

• y = mx + c

Where does the y-intercept occur on a graph?

• Where y is 0

• Where x is 0

• Where x is 1

• Where y is 1

What is the rate of change in a linear relationship?

• Change in x over change in y

• Change in y over change in x

• Sum of x and y

• Difference between x and y

What is the first step in writing an equation from a graph?

• Draw the graph

• Calculate the slope

• Create a table of ordered pairs

• Identify the y-intercept

If the change in y is 2 and the change in x is 1, what is the rate of change?

• 3

• 0.5

• 2

• 1

In the equation y = 2x + 1, what is the y-intercept?

• -1

• 0

• 1

• 2

For the equation y = 1/2x - 2, what is the slope?

• -1/2

• 1/2

• -2

• 2

If the change in y is -3 and the change in x is 1, what is the rate of change?

• 3

• -3

• 1

• -1

In the equation y = -3x - 3, what is the y-intercept?

• 3

• -1

• 0

• -3

What is the rate of change if the change in y is -3 and the change in x is 4?

• -3/4

• 3/4

• -4/3

• 4/3