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Sec 3.7 Equations of Lines in the Coordinate Plane Chapter 3 Review If two lines are cut by a transversal they form special properties. Corresponding angles Alternate interior angles Alternate exterior angles Are congruent. Are parallel Same-side interior angles are supplementary. Two lines to the same line are to each other. In a plane, two lines to the same line are . Lesson Purpose Objective Essential Write How an equation of a line given characteristics of parallel or perpendicular lines. Question can you prove that two lines are parallel? What is a slope? The steepness of a hill Different types of slopes A positive(+) slope: A negative(-) slope: If you go from left to right and you go up, it is a positive slope If you go from left to right and you go down, it is a negative slope A zero (0) slope: If you go from left to right and you don't go up or down, it is a zero slope No Slope or Slope Undefined Vertical lines have no slope, or undefined slope. Ski Bird cannot ski vertically. Sheer doom awaits Ski Bird at the bottom of a vertical hill. Slope Equation A slope of a line contains two points (x₁, y₁) and (x₂ ,y₂). Example #1 Let’s find the slope of the line passing through the given points. (2,3),(-1,-6) Step 1: use slope equation: Step 2: set up equation with points given: Step 3: solve What kind of slope is it? Question #1 What is the slope of the line passing through the points (2, 7) and (21, 3)? A. 2/7 B. 3/4 C. 4/3 D. 1/3 Question #2 What is the slope of the line passing through the points (-2,-3) and (1, 3)? A. 1/2 B. 2 C. -2 D. -1/2 Example #2 What is the slope of the line? Question #3 Find the slope of the line? A. 1/4 B. -1/4 C. -4 D. 4 Question #4 Find the slope of the line? A. 2/3 B. 3/2 C. -2/3 D. -3/2 3.8 Slopes of Parallel lines Parallel lines have the same slope. Slopes of Perpendicular Lines The product of the slopes of two perpendicular lines is -1 or the slopes are negative reciprocal. Product means multiplication. Slope-Intercept Form -is an equation of a non-vertical line is y=mx+b where m is the slope and b is y-intercept Example #3 Graph the equation of the line y= ½x+2 Step 1: identify the slope and yintercept Step 2 : plot your y- intercept Step 3: connect the points Question #5 Graph A. C. the equation y= ½x-3 B D. Question #6 Graph A C the equation y= -2x-2 B D Real World Connections Ticket Out and Homework Is it always necessary to identify both the slope and y-intercept of a line when graphing its equation? Explain pg. 207-208 #’s 5, 6, 7,9,10, 14, 15, 18,19,20,21