1. Five-Minute Check (over Lesson 2–7) Mathematical Practices Then/Now
New Vocabulary
Key Concept: Slope of a Line
Example 1: Find the Slope of a Line
Example 2: Use Slope and a Point on the Line
Postulates: Parallel and Perpendicular Lines
Example 3: Determine Line Relationships
Example 4: Real World Example: Write Equations of Parallel or Perpendicular Lines
Lesson Menu

2. Classify the relationship between 1 and 5.
A. corresponding angles
B. vertical angles
C. consecutive interior angles
D. alternate exterior angles
5-Minute Check 1

3. Classify the relationship between 4 and 6.
A. alternate interior angles
B. alternate exterior angles
C. corresponding angles
D. vertical angles
5-Minute Check 2

4. In the figure, m4 = 146. Find the measure of 7.
B. 34
C. 146
D. 156
5-Minute Check 3

5. In the figure, m4 = 146. Find the measure of 10.
B. 146
C. 56
D. 34
5-Minute Check 4

6. In the figure, m4 = 146. Find the measure of 11.
B. 160
C. 52
D. 34
5-Minute Check 5

7. In the map shown, 5th Street and 7th Street are parallel
In the map shown, 5th Street and 7th Street are parallel. At what acute angle do Strait Street and Oak Avenue meet?
A. 76
B. 75
C. 53
D. 52
5-Minute Check 6

8. Mathematical Practices
1 Make sense of problems and persevere in solving them.
4 Model with mathematics.
Content Standards
G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). MP

9. Use slope to identify parallel and perpendicular lines.
You used the properties of parallel lines to determine congruent angles.
Find the slope of a line and use slope to write the equation of a line.
Use slope to identify parallel and perpendicular lines.
Then/Now

10. slope
slope-intercept form
point-slope form
Vocabulary

11. Concept

12. A. Find the slope of the line.
Find the Slope of a Line
A. Find the slope of the line.
Substitute (–3, 7) for (x1, y1) and (–1, –1) for (x2, y2).
Slope formula
Substitution
Subtract.
Simplify.
Answer: –4
Example 1

13. B. Find the slope of the line.
Find the Slope of a Line
B. Find the slope of the line.
Substitute (–2, –1) for (x1, y1) and (6, –1) for (x2, y2).
Slope formula
Substitution
Subtract.
Simplify.
Answer: 0
Example 1

14. A. Find the slope of the line.B. C. D.
Example 1a

15. B. Find the slope of the line.
A. 0
B. undefined
C. 7 D.
Example 1b

16. C. Find the slope of the line.A. B.
C. –2
D. 2
Example 1c

17. D. Find the slope of the line.
A. 0
B. undefined
C. 3 D.
Example 1d

18. Use Slope and a Point on the Line
Write an equation in point-slope form of the line whose slope is that contains (–10, 8). Then graph the line.
Point-slope form
Simplify.
Example 2

19. Graph the given point (–10, 8).
Use Slope and a Point on the Line
Answer:
Graph the given point (–10, 8).
Use the slope to find another point 3 units down and 5 units to the right.
Draw a line through these two points.
Example 2

20. Write an equation in point-slope form of the line whose slope is that contains (6, –3).B. C. D.
Example 2

21. Concept

22. Step 1 Find the slopes of and .
Determine Line Relationships
Determine whether and are parallel, perpendicular, or neither for F(1, –3), G(–2, –1), H(5, 0), and J(6, 3). Graph each line to verify your answer.
Step 1 Find the slopes of and
Example 3

23. Step 2 Determine the relationship, if any, between the lines.
Determine Line Relationships
Step 2 Determine the relationship, if any, between the lines.
The slopes are not the same, so and are not parallel. The product of the slopes is So, and are not
perpendicular.
Example 3

24. Answer: The lines are neither parallel nor perpendicular.
Determine Line Relationships
Answer: The lines are neither parallel nor perpendicular.
Check When graphed, you can see that the lines are not parallel and do not intersect in right angles.
Example 3

25. Determine whether AB and CD are parallel, perpendicular, or neither for A(–2, –1), B(4, 5), C(6, 1), and D(9, –2)
A. parallel
B. perpendicular
C. neither
Example 3

26. The section of track modeled by the line
Write Equations of Parallel or Perpendicular Lines
MODEL RAILROADS A plan for a model railroad shows a straight section of track along the line
A second straight section of track is perpendicular to the first and passes through (2, 0). Write an equation in slope-intercept form for the second section of track.
The section of track modeled by the line
has a slope of so the second section of track will have a slope of –5 and pass through (2, 0)
Example 4

27. y = mx + b Slope-Intercept form 0 = –5(2) + b m = –5, (x, y) = (2, 0)
Write Equations of Parallel or Perpendicular Lines
y = mx + b Slope-Intercept form
0 = –5(2) + b m = –5, (x, y) = (2, 0)
0 = –10 + b Simplify.
10 = b Add 10 to each side.
Substitute m and b into the slope intercept form of a line.
So, the equation of the second track is y = –5x + 10.
Answer: So, the equation is y = –5x + 10.
Example 4

28. A. y = 3x
B. y = 3x + 8
C. y = –3x + 8 D.
Example 4