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Lesson Menu 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

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CCSS 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.

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

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Vocabulary slope rate of change

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Concept

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Example 1 Find the Slope of a Line A. Find the slope of the line. Substitute (–3, 7) for (x 1, y 1 ) and (–1, –1) for (x 2, y 2 ). Answer:–4 Slope formula Substitution Simplify.

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Example 1 Find the Slope of a Line B. Find the slope of the line. Substitute (0, 4) for (x 1, y 1 ) and (0, –3) for (x 2, y 2 ). Answer:The slope is undefined. Slope formula Substitution Simplify.

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

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

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

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

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

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

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Concept

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Example 3 Determine Line Relationships Step 1Find the slopes of and. 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.

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Example 3 Determine Line Relationships Step 2Determine 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.

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

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

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

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

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Example 4 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

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End of the Lesson

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