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