Linear Functions and Their Applications

This video tutorial explains how to write linear equations in slope-intercept form to model real-world situations. It covers the basic form of the equation, y = mx + b, where m is the slope and b is the vertical intercept. Two examples are provided: one modeling the depreciation of a TV's value over time and another modeling the increase in tuition costs at a university. The tutorial demonstrates how to identify the slope and intercept from given data and construct the corresponding linear function.

What is the general form of a linear equation in slope-intercept form?

• y = mx + b

• y = ax^2 + bx + c

• y = a/x + b

• y = ax + b

In the context of application problems, what is the slope often referred to as?

• Initial value

• Horizontal intercept

• Rate of change

• Vertical intercept

What is the initial value of the TV in the first example?

• $2,050

• $2,550

• $250

• $2,300

How does the value of the TV change each year?

• Decreases by $2,300

• Increases by $2,300

• Decreases by $250

• Increases by $250

What is the equivalent function form for the TV's value over time?

• V(t) = 250t - 2,300

• V(t) = 2,300 + 250t

• V(t) = 250 + 2,300t

• V(t) = 2,300 - 250t

In the second example, what is the cost per credit hour in 1998?

• $180

• $238

• $144

• $200

How many years after 1990 is the year 2008?

• 28 years

• 18 years

• 38 years

• 8 years

What is the slope of the tuition cost equation?

• 940

• 0.94

• 94

• 9.4

What does the slope represent in the context of the tuition cost example?

• The initial cost

• The total cost

• The rate of increase per year

• The decrease in cost

What is the vertical intercept in the tuition cost equation?

• 238

• 68.8

• 9.4

• 144