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2.3 – Linear Functions
Objectives
 Describe linear functions with words, graphically, with a table of values, or with an algebraic expression.
 Identify and interpret the slope and intercept of a line.
 Write equations of lines.
Key Terms & Notes
Parallel & Perpendicular Lines 
 Parallel lines have equal slopes.
 Ex. The following lines are parallel because they have the same slope.
 Perpendicular lines have negative reciprocal slopes.
 Ex. The following lines are perpendicular because their slopes are negative reciprocals of one another. This means that the slopes are flipped and one is positive while the other is negative.

Examples
 Ex 1. What is the slope of a line is parallel to ?
 Answer:

 Ex 2. What is the graph of the line ?
 Answer: There is a negative slope and a negative yintercept, so the line crosses the yaxis at 2 and slopes down from left to right.

 Ex 3. What is the slope of the function, represented by the table of values below?
Answer: Pick any two points in the chart and use the slope formula:

 Ex 4. Which of the following is the equation of a line that passes through the point (1,4) and is parallel to the xaxis?
 Answer: The xaxis has a zero slope, so substitute into the pointslope form: .
 This becomes , which simplifies to .

 Ex 5. Which of the following is the equation of a line that passes through the points (0,6) and (2,10)?
 To solve this, do the following steps:
 Find the slope: , which simplifies to .
 Put the slope and ONE of the points into pointslope form: .
 Use distribution and inverse operations to convert to slopeintercept form: , and then again to .
 Answer:

 Ex 6. Jenny is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her own expenses. After a month of driving from neighborhood to neighborhood and walking doortodoor, she figures out that her weekly earnings are approximately a linear function of the number of doors she knocks on. She writes the equation of the function like this: , where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars.
 What does the slope of Jenny’s function represent?
 Answer: for each additional door she knocks on, her earnings will increase by $20.
 This is because the slope represents how much money she makes PER (each) door she knocks on. For every door, she makes $20 more dollars. You can multiply 20 times the number of doors knocked on. That’s why it is written as 20 times x.
 The $50 represents her base salary (and therefore, her expenses) for the week… it is not the slope. If she doesn’t knock on any doors, she will actually lose (minus) the $50 and not be able to pay for her expenses.

 Ex 7. The ordered pairs below represent a relation between x and y.
 (3,0), (2,4), (1,8), (0,12), (1,16), (2,20)
 Could this set of ordered pairs have been generated by a linear function?
 Answer: Yes, because the relative difference between yvalues and xvalues is the same no matter which pairs of (x, y) values you use to calculate it.
 In other words, the slope is the same for any two points you calculate. So, you have a line, which is represented by a linear function!

Important!
Practice (Apex Study 2.3)
 Practice: Pg 8, 9, 14, 15
 Understand the TShirt problem on Pg 10
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