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Parallel and Perpendicular Lines The goal of this lesson is to discover what the relationship is between sets of parallel lines and between sets of perpendicular lines. This will help us to write equations that describe parallel or perpendicular lines in the future. Phase 1- Parallel lines 1. Open up Geogebra and draw a line that goes through 2 points. Write the points and the equation here: ( , ) and ( , ). Equation: 2. Use the “draw parallel line” function to draw a parallel line through the point (-2,2). Write the equation of the new line here: 3. Use the “draw parallel line” function to draw a parallel line through the point (5,-1). Write the equation of the new line here: 4. Continue exploring the relationship between parallel lines until you can answer the question, “What do all lines that are parallel to one another have in common?” Restart the process from step 1 using 2 new points if necessary. Application: Use what you now know about parallel lines to write the equation of a line parallel to the one given and through the given point. 1. Write the equation of a line that is parallel to y = 2x + 3 and passes through the points (0,0). 2. Write the equation of a line that is parallel to y = ½ x + 5 and passes through the points (1,4). 3. Write the equation of a line that is parallel to y = -1/4 x – 6 and passes through the points (1,4). 4. Write the equation of a line that is parallel to y = - 6x + 2 and passes through the points ( -2, -3) Part II. Without a computer. Do this algebraically 1) Find the equation of line parallel to y = 4x + 5 that goes through the point (2,8) ? What is the slope of this new equation’s line? What point does it go through? Now, use your prior knowledge to answer this question algebraically 2) Find the equation of line parallel to y = 3x + 1 that goes through the point (2,8) ? 3) Find the equation of line parallel to y = 2x +7 and that goes through the point (4 , 12) ? 4) Find the equation of a line parallel to y =4x + 12 that goes through the point (1,9) ? 5) Find the equation of a line parallel to y =4x + 12 that goes through the point (-2 , 3) ? Homework: 1) Find the equation of a line parallel to y = 10x – 2 that goes through the point (2,5)? 2) Find the equation of a line parallel to y = 7x — 3 that goes through point (2,17 )? Are the pairs of lines below parallel? Justify your answer mathematically 3) Line 1: 2y = 2x +4 Line 2: y – 2x = 7 4) Line 1: 3y = 3x + 5 Line 2: y – x = 2 5) Find the equation of a line through the points (1,2) and (-1,6) 6) Find the equation of a line through the points (4,3) and (8,1) 7) 2 2 5 3 2 2 8) 5 7