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Do Now 11/30/09

Do Now 11/30/09. Copy HW in your planner. Text p. 322, #8-24 even, 32 & 36 Open your textbook to page 318 and complete the “If-Then Statement” Activity. With your partner make one set of “cards.” Then answer the questions in your notebook. Objective.

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Do Now 11/30/09

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  1. Do Now 11/30/09 • Copy HW in your planner. • Text p. 322, #8-24 even, 32 & 36 • Open your textbook to page 318 and complete the “If-Then Statement” Activity. With your partner make one set of “cards.” Then answer the questions in your notebook.

  2. Objective • SWBAT write equations of parallel and perpendicular lines.

  3. If-Then Statements and Their Converses IF-THEN STATEMENTS… - “IF” stands for a hypothesis - “THEN” stands for a conclusion CONVERSE… - the converse of a conditional statement INTERCHANGES the hypothesis and conclusion. The converse of a true statement is not always necessarily true. If it is a duck, then it has wings. All ducks have wings. If it is has wings, then it is a duck. Airplanes have wings and it is not a duck.

  4. Section 5.5 “Write Equations of Parallel and Perpendicular Lines” • PARALLEL LINES • If two nonvertical lines in the same plane have the same slope, then they are parallel. • If two nonvertical lines in the same plane are parallel, then they have the same slope.

  5. Write an equation of the line that passes through (–3,–5)and is parallel to the liney= 3x– 1. STEP1 Identify the slope. The graph of the given equation has a slope of 3. So, the parallel line through (– 3, – 5) has a slope of 3. STEP2 Find the y-intercept. Use the slope and the given point. y= mx+ b Write slope-intercept form. – 5= 3(– 3) + b Substitute3form, -3for x,and -5fory. 4 = b Solve forb. STEP3 Write an equation. Usey = mx + b. y = 3x + 4 Substitute3formand4forb.

  6. Write an equation of the line that passes through (–2,11)and is parallel to the liney= -x + 5. STEP1 Identify the slope. The graph of the given equation has a slope of -1. So, the parallel line through (– 2, 11) has a slope of -1. STEP2 Find the y-intercept. Use the slope and the given point. y= mx+ b Write slope-intercept form. 11= -1(–2) + b Substitute-1form, -2for x,and 11 fory. 9 = b Solve forb. STEP3 Write an equation. Usey = mx + b. y = -x+ 9 Substitute-1formand9forb.

  7. PERPENDICULAR LINES • If two nonvertical lines in the same plane have slopes that are negative reciprocals, then the lines are perpendicular. • If two nonvertical lines in the same plane are perpendicular, then their slopes are negative reciprocals ½ and -2 are negative reciprocals. 3 and -1/3 are negative reciprocals.

  8. Determine which lines, if any, are parallel or perpendicular. – x y = + 1 2 1 5 5 5 x – y = Line a: y = 5x – 3 Line b:x +5y = 2 Line c:–10y – 2x = 0 Find the slopes of the lines. Write the equations for lines a, b, and cin slope-intercept form. Linea: y = 5x – 3 Lineb: x + 5y = 2 Linec: – 10y – 2x = 0 5y = – x + 2 – 10y = 2x Lines band chave slopes of –1/5, so they are parallel. Linea has a slope of 5, the negative reciprocal of –1/5, so it is perpendicular to lines band c.

  9. Determine which lines, if any, are parallel or perpendicular. 1 1 3 2 – – x y = Line a: 2x + 6y = -3 Line b:3x – 8 = y Line c:–1.5y + 4.5x = 6 Find the slopes of the lines. Write the equations for lines a, b, and cin slope-intercept form. 2x + 6y = -3 3x – 8 = y –1.5y + 4.5x = 6 Linea: Lineb: Linec: – 1.5y = -4.5x + 6 6y = –2x – 3 y = 3x – 4 Lines band chave slopes of 3, so they are parallel. Linea has a slope of -1/3, the negative reciprocal of 3, so it is perpendicular to lines band c.

  10. y= mx+ b 1 – (4) + b – 5= Substitute – for m, 4 for x, and – 5 for y. 2 Identify the slope. The graph of the given equation has a slope of 2. Because the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line through (4, –5) is -1/2 . 1 2 – 3= b 1 2 1 y = – x – 3 Substitute – formand–3for b. 2 Write an equation of the line that passes through(4, – 5)and is perpendicular to the liney = 2x+ 3. STEP1 STEP 2 Find the y-intercept. Use the slope and the given point. Write slope-intercept form. Solve for b. STEP3 y = m x + b Write slope-intercept form. Write an equation.

  11. Homework • Text p. 322, #8-24 even, 32 & 36

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