Exploring Applications of Linear Functions

The video tutorial explains how to apply linear functions to real-world situations. It covers the characteristics of linear functions, such as constant rate of change, and how to identify and use different forms of linear equations, including slope-intercept and point-slope forms. Examples include modeling savings growth, a child's weight gain, and taxi ride costs. The tutorial emphasizes understanding when to use each form based on available data points.

What identifies a linear function?

• No change over time

• Decreasing rate of change

• Constant rate of change

• Variable rate of change

Which formula is used when the starting point and rate of change are known?

• Slope-intercept formula

• Point-slope formula

• Quadratic formula

• None of the above

What does the 'B' in the slope-intercept equation represent?

• End point

• Rate of change

• Starting point

• Slope

How is the slope calculated when two points are known?

• x1 + x2 / y1 + y2

• y1 + y2 / x1 + x2

• x2 - x1 / y2 - y1

• y2 - y1 / x2 - x1

What equation models the savings account growth?

• y = 150x + 28

• y = 28x + 150

• y = 150x - 28

• y = 28x - 150

What form is used when the initial weight of the child is unknown?

• Slope-intercept form

• Linear form

• Point-slope form

• Quadratic form

After converting to slope-intercept, what is the child's weight equation?

• y = 7.7x + 2.4

• y = 2.4x + 7.7

• y = 2.4x - 7.2

• y = 7.2x - 2.4

What is the slope found for the taxi ride cost?

• 1/2

• 2/3

• 4/5

• 5/4

What is the final form of the taxi ride cost equation?

• y = 4/5x + 4

• y = 5/4x + 4

• y = 4/5x - 4

• y = 5/4x - 4

How can you model real-world situations with linear functions?

• Linear functions cannot model real-world situations

• Using the slope and/or y-intercept based on available data

• Using only the y-intercept

• Using only the slope