1. Lesson 1.1 Lines in the Plane
Essential Question: How do you calculate the slope of a line?
How do you write the equation of a line?

2. What is slope?
The ratio of the vertical change, the rise, to the horizontal change, the run.
The change in y over the change in x.
𝐫𝐢𝐬𝐞 𝐫𝐮𝐧

3. The slope of a nonvertical line represents the number of units the line rises or falls vertically for each unit of horizontal change from left to right.

4. How do you calculate the slope of a line?
You use the slope formula

5. Find the slope of the line passing through each pair of points.
a. (–2, 0) and (3, 1)
b. (–1, 2) and (2, 2)
c. (0, 4) and (1, –1)

6. 4 Types of Slope
A line with …a positive slope (𝑚>0) rises from left to right. …a negative slope (𝑚<0) falls from left to right …zero slope (𝑚=0) is horizontal …undefined slope is vertical

7. What type of slope can a line have?
Positive
Negative
Zero
Undefined

8. Point – Slope Equation of a Line
Use this when a slope and a point is known. m is the slope and (x1, y1) is the point you know. Vertical lines can’t be written using this form. This is sometimes called the two-point form of the equation of a line.

9. How do you write an equation of a line?
Write point-slope form.
If necessary, calculate the slope.
Substitute the values for the slope and the point.
Rewrite the equation for y.

10. Find the equation of the line whose slope is 3 and passes through the point (1, −2).

11. Find the equation of the line whose slope is 2 and passes through the point (3, −7).

12. During 2006, Research in Motion’s net profits were $631
During 2006, Research in Motion’s net profits were $631.6 million, and in 2007 net profits were $ million. Write a linear equation giving the net profits y in terms of the year x. Then use the equation to predict the net profits for 2008.

13. The net sales for a car manufacturer were $14
The net sales for a car manufacturer were $14.61 billion in 2009 and $15.78 billion in Write a linear equation giving the net sales y in terms of x, where x is the number of years since Then use the equation to predict the net sales for 2011.

14. What is a parent function?
The most basic function in a family
The parent linear function is 𝑓 (𝑥) = 𝑥

15. Library of Parent Functions: Linear Function
Graph of 𝑓 𝑥 =𝑥
Domain: −∞, ∞
Range: −∞, ∞
Intercept: 0, 0
Increasing
The function 𝑓 𝑥 =𝑥 is also referred to as the identity function.

16. Sketching Graphs of Lines
Many problems in coordinate geometry can be classified as follows. 1. Given a graph (or parts of it), find its equation. 2. Given an equation, sketch its graph.

17. Slope-Intercept Form of the Equation of a Line
The graph of the equation
𝑦=𝑚𝑥+𝑏
is a line whose slope is m and whose y-intercept is 0, 𝑏 .

18. Determine the slope and y-intercept of the linear equation 𝑥+𝑦=2
Determine the slope and y-intercept of the linear equation 𝑥+𝑦=2. Then describe its graph.

19. Determine the slope and y-intercept of the linear equation −4𝑥−𝑦+5=0
Determine the slope and y-intercept of the linear equation −4𝑥−𝑦+5=0. Then describe its graph.

20. Summary of Equations of Lines
General Form
𝐴𝑥+𝐵𝑦+𝐶=0
Vertical Line
𝑥=𝑎
Horizontal Line
𝑦=𝑏
Slope-Intercept Form
𝑦=𝑚𝑥+𝑏
Point-Slope Form
𝑦− 𝑦 1 =𝑚 𝑥− 𝑥 1

21. Graphing Calculators
Use a graphing utility to graph the line 𝑦=−𝑥+2, first using a viewing window in which the slope visually appears to be – 1, and then using one in which the slope does not visually appear to be – 1. Explain why the slope appears to be correct in the first graph.

22. Parallel and Perpendicular Lines
The slope of a line is a convenient tool for determining whether two lines are parallel or perpendicular.
Two distinct non vertical lines are
parallel if and only if their slopes are equal
perpendicular if and only if their slopes are opposite reciprocals

23. Find the slope-intercept form of the equations of the lines that pass through (2, −1) and are: Parallel to 2𝑥−3𝑦=5 Perpendicular to 2𝑥−3𝑦=5

24. Find the slope-intercept form of the equations of a line that pass through (2, 1) and are: Parallel to 4𝑥−2𝑦=3 Perpendicular to 4𝑥−2𝑦=3

25. Use a graphing utility to graph the lines 𝑦=2𝑥+6 and 𝑦=− 1 2 𝑥+4, first using a viewing window that is square and then using one that is nonsquare. The lines are supposed to be perpendicular. What is the difference, if any? Which viewing window correctly displays the answer?

26. How do you calculate the slope of a line
How do you calculate the slope of a line? How do you write the equation of a line?

27. Ticket Out the Door
Write an equation of the line that passes through the points −2,1 and 3,2