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**Five-Minute Check (over Lesson 3–2) CCSS Then/Now New Vocabulary **

Key Concept: Slope of a Line Example 1: Find the Slope of a Line Concept Summary: Classifying Slopes Example 2: Real-World Example: Use Slope as Rate of Change Postulates: Parallel and Perpendicular Lines Example 3: Determine Line Relationships Example 4: Use Slope to Graph a Line Lesson Menu

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**Mathematical Practices 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). Mathematical Practices 4 Model with mathematics. 7 Look for and make use of structure. 8 Look for and express regularity in repeated reasoning. CCSS

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**Use slope to identify parallel and perpendicular lines.**

You used the properties of parallel lines to determine congruent angles. Find slopes of lines. Use slope to identify parallel and perpendicular lines. Then/Now

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slope rate of change Vocabulary

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Concept

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Concept

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**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 Simplify. Answer: –4 Example 1

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**B. Find the slope of the line.**

Find the Slope of a Line B. Find the slope of the line. Substitute (0, 4) for (x1, y1) and (0, –3) for (x2, y2). Slope formula Substitution Simplify. Answer: The slope is undefined. Example 1

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**C. Find the slope of the line.**

Find the Slope of a Line C. Find the slope of the line. Substitute (–2, –5) for (x1, y1) and (6, 2) for (x2, y2). Slope formula Substitution Simplify. Answer: Example 1

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**D. Find the slope of the line.**

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

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**A. Find the slope of the line.**

B. C. D. Example 1a

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**B. Find the slope of the line.**

A. 0 B. undefined C. 7 D. Example 1b

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**C. Find the slope of the line.**

A. B. C. –2 D. 2 Example 1c

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**D. Find the slope of the line.**

A. 0 B. undefined C. 3 D. Example 1d

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Concept

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**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

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**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

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**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

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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

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**Use Slope to Graph a Line**

Graph the line that contains Q(5, 1) and is parallel to MN with M(–2, 4) and N(2, 1). First, find the slope of Slope formula Substitution Simplify. Example 4

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**The slopes of two parallel lines are the same.**

Use Slope to Graph a Line The slopes of two parallel lines are the same. The slope of the line parallel to through Q(5, 1) is Answer: Graph the line. Start at (5, 1). Move up 3 units and then move left 4 units. Label the point R. Draw Example 4

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**Graph the line that contains R(2, –1) and is parallel to OP with O(1, 6) and P(–3, 1).**

A. B. C. D. none of these Example 4

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End of the Lesson

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EXAMPLE 1 Write an equation of a line from a graph

EXAMPLE 1 Write an equation of a line from a graph

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