applications of linear equations example 1: joel is renting an apartment for $465 a month. he must...
TRANSCRIPT
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.
