Applications of Linear Equations Example 1: Joel is renting an apartment for $465 a month. He must pay a $300 non-refundable deposit since he has a dog. a) Write the equation for the amount A that Joel pays in rent for x months. The $300 is a fixed cost – that amount won’t change. The $465 is a variable cost – how much Joel pays depends on the number of months rented.

Number of Months Cost per Month Cost for Monthly Rent ∙465= ∙465=1395 ……… x465x∙465 Joel is renting an apartment for $465 a month. He must pay a $300 non-refundable deposit since he has a dog. (Amount paid)= (Variable costs)+ (Fixed costs)

Joel is renting an apartment for $465 a month. He must pay a $300 non-refundable deposit since he has a dog. b) Use the equation to predict the cost of renting the apartment for three years. 3 years = 3∙12 = 36 months The total cost for a three year rental will be $17,040

Applications of Linear Equations Example 2: The following graph shows the results of a particular study determining the average height of trees in inches a given number of years after the study began.

# of years since study began height in inches

a) Write the equation of the line in slope- intercept form. Use the two given points to find the slope:

Use the first point and the slope to write the point-slope form: The equation of the line in slope-intercept form is given by

b) Find the y-intercept and explain what it means in light of the application. y-intercept: Review the graph and locate this point on the graph.

# of years since study began height in inches The horizontal axis is years. The vertical axis is height.

Meaning in the application: Ordered pair from the equation: The average height of the trees at the beginning of the study (0 years) was 26 inches tall. y-intercept:

c) Determine the slope and explain what it means in light of the application. Slope: The average height of the trees increased at a rate of 3 inches per year.