Constructing Linear Functions: Finding Initial Value and Rate of Change

This lesson teaches how to construct linear functions by solving for unknowns. It covers the components of a linear function, such as initial value and rate of change, and how to use these to form equations. The video explains how to analyze graphs to find these values and construct equations using known points, a single point with a rate of change, or two points. The lesson emphasizes understanding the relationship between input and output changes to determine the slope and y-intercept, ultimately forming the equation of a line.

What are the two key components that define a linear relationship?

What does the 'm' represent in the equation of a line?

How do you determine the initial value in a linear function?

Explain how to calculate the rate of change using a graph.

How can you find the initial value if you only know the rate of change?

What is the equation of the line if the initial value is 1 and the rate of change is 2?

Describe the process of constructing an equation when given two points on a graph.