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LO SWBAT write the equation of a line that contains a given point and is perpendicular to a given line. A.2(F) 1 DOL Given 4 equations or graphs, students will identify the perpendicular slope or write equations of perpendicular lines correctly at least 3 times. 2 Warm Up – Wednesday 10/28 1. The line to the right is shifted up 4 units. What is the equation of the resulting line written in the form y = mx + b? 2. Which line is parallel to 3y + 2x = 12? A. 6x – 4y = 24 C. 2x + 3y = 6 B. y + 3x = -2 D. y = -2x + 6 3. Can parallel lines have the same y-intercept? Explain why or why not. 3 This Week: • HW Due Tomorrow Make sure to SHOW WORK 4 Tutoring This Week Morning (8:05 – 8:40 AM) Afternoon (4:15 – 4:45 PM) Monday Tuesday Wednesday Thursday Friday Saturday Saturday School 5 Today’s Goal: SWBAT write the equation of a line that contains given point and is perpendicular to a given line. A.2(F) Our Goals This Week: Be Good Citizens 100% Exit ticket 70% HW 90% Why This Matters Perpendicular lines are a part of every day. They are present in something as simple as certain letters of the alphabet to the streets and buildings we encounter in our everyday travel. 6 Parallel Lines • Never intersect • Have the same slope • Notation: l1 || l2 y = 3x + 5 y = 3x – 7 y = 3x + 0.5 y = 3x l1 ALL of these lines are parallel. l2 They all have the SAME slope(m). 7 Perpendicular Lines • Lines that intersect at right angles. • Lines that have slopes that are opposite reciprocals of each other. (sometimes called negative reciprocals) • The product of the two slopes equals -1. • Symbolic Notation: l1 l2 8 Where do you see Perpendicular Lines in everyday life? 9 Quick Check – Partner Talk With a partner, the person who is the younger of the two will explain the properties of parallel lines and the other person will explain the properties of perpendicular lines. 10 Perpendicular Right Angels 1 2 4 3 11 Negative opposite Product This is how you test the slope + – 12 So What does OPPOSITE RECIPROCALS mean? The term Opposite Reciprocals refers to two numbers that have different signs and are flipped fractions of each other. 5 1 −3 7 5 − 1 3 7 1 − 5 7 3 13 Check Yourself! The product of the slopes of perpendicular lines is always -1! 5 1 3 − 7 1 −5 − = 5 5 −21 7 = 21 3 = -1 = -1 14 Now You Try 1 6 6 − 1 5 − 8 8 5 Don’t forget to check the products of the slopes. 15 Quick Check On your whiteboards, create one positive and one negative fraction and show the opposite reciprocal of each one. You MAY NOT use one that we have already done! 16 Compare the Slopes Find the rate of change of AB. 𝟒 𝑦 𝑟𝑖𝑠𝑒 Rate of change = = = 𝑥 𝑟𝑢𝑛 𝟏 4 4 -1 1 Find the rate of change of CD. −𝟏 𝑦 𝑟𝑖𝑠𝑒 Rate of change = = = 𝑥 𝑟𝑢𝑛 𝟒 17 Perpendicular… These lines are parallel. Why? Because their slopes are opposite reciprocals of each other. 18 Compare the Slopes Find the rate of change of AB. 𝟑 𝑦 𝑟𝑖𝑠𝑒 Rate of change = = = 𝑥 𝑟𝑢𝑛 𝟐 2 -1 3 2 Find the rate of change of CD. −𝟏 𝑦 𝑟𝑖𝑠𝑒 Rate of change = = = 𝑥 𝑟𝑢𝑛 𝟐 19 Neither… The slopes of AB and CD are not equal and are not opposite reciprocals. …so they are neither parallel nor perpendicular. 20 Forms of Linear Equations 21 Guided Practice a. Write the equation to a line in slope-intercept form perpendicular to the graph of y = -4x + 5 and contains the point (1,-3). Original Equation New Equation y = -4x + 5 m= m = -4 Point (1, -3) 22 Guided Practice b. A line w contains the points (1, 1) and (-1, 2). Write the equation of line p perpendicular to line w passing through (-2, -1). Original Equation New Equation (1, 1) and (-1, 2) m= m=? Point (-2, -1) 23 Independent practice Directions • Do at least 7 problems. • If you have a question, ASK! • Check work at the board, help your neighbor. • You will be turning this in for a grade. 24 DOL 1) What is the slope of the line perpendicular to 2x + y = -8? −𝟐 2) What is the slope of the line perpendicular to y – 5 = (x + 6)? 𝟑 3) Write the equation of a line in slope-intercept form that is 𝟏 perpendicular to y = x + 6 and whose y-intercept is (0, 12). 𝟕 4) Write an equation of the line in slope-intercept form that is perpendicular to the graph below and passes through point C. C 25