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

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

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

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

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

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

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

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

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

slope slope-intercept form point-slope form Vocabulary

Concept

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

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

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

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

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

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

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

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

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

Concept

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

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

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

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

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

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

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