Applications of Linear Equations

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 forMonthly Rent

1 465 465

2 465 2∙465=930

3 465 3∙465=1395

… … …

x 465 x∙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)

A 465 x 300

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.

A 465 300x

3 years = 3∙12 = 36 months

36465 300 16740 300 17040

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

heig

ht in

inch

es

(3,35)

(8,50)

a) Write the equation of the line in slope-intercept form.

Use the two given points to find the slope:

(3,35)

(8,50)

2 1

2 1

y ym

x x

50 35

8 3

15

5

3

Use the first point and the slope to write the point-slope form:

(3,35) 1 1( )y y m x x

3m 35 3( 3)y x

35 3 9y x

3 26y x

The equation of the line in slope-intercept form is given by 3 26y x

b) Find the y-intercept and explain what it means in light of the application.

3 26y x

y-intercept: (0, 26)

Review the graph and locate this point on the graph.

# of years since study began

heig

ht in

inch

es

(3,35)

(8,50)

(0, 26)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.

( , )x y

( , )years inches

y-intercept: (0, 26)

c) Determine the slope and explain what it means in light of the application.

3 26y x

Slope: 3m

2 1

2 1

y ym

x x

changein y

changein x changein height

changein years

3

1m

The average height of the trees increased at a

rate of 3 inches per year.