Geometry • Agenda 1. ENTRANCE 2. Go over Practice 3. 3-5 Continued 4. Practice 5. EXIT Practice Chapter 3 3-5 Continued Slope • The steepness of a line • ryse run y2 y1 • m x2 x1 ( x2 , y2 ) ( x1 , y1 ) Types of Slope • Positive • Negative • Zero • No Equations of Lines • A line is a set of points. Every line has an equation that relates the coordinates of these points. ex: 2x - 3y = 14 (1, -4) (4, -2) (2.5, -3) (-2, -6) (-0.5, -5) (7, 0) Forms of a Line • These are each different forms of the same equation. 2x - 3y = 14 Standard form 2 14 y = x 3 3 Slope-Intercept form 2 y + 4 = (x -1) 3 Point-Slope form Standard Form • This equation is of the form Ax + By = C. The x and y terms are on the left side and the constant is on the right side of the equation. 2x - 3y = 14 Slope-Intercept Form • This equation is of the form y = mx + b. The y term is on the left and the x term is on the right side of the equation. The value of m is the slope of the equation. The value of b is the y-intercept. 2 14 y = x 3 3 Point-Slope Form • This equation is of the form y – y1 = m(x – x1). The y term is on the left and the x term is on the right side of the equation. The value of m is the slope of the equation. The values x1 and y1 are the coordinates of a point on the line. 2 y + 4 = (x – 1) 3 2 m= (1, -4) 3 Example #1 • Graph. 2 y x 1 3 Example #2 • Graph. 3x 2 y 6 Example #3 • Graph. x 2y 4 Example #4 • Find the equation of a line with slope -3 that contains the point (-1, 4). Example #5 • Find the equation of a line that contains the points (6, 3) and (-4, 5). Example #6 • Find the equation of a horizontal line through the point (-3, 1). Example #7 • Find the equation of a vertical line through the point (1, -2). Example #8 • A truck ramp is being redesigned for a local moving company. What is the equation of the line that represents the ramp? Example #9 • The equation P = $300m + $2000 represents the total payment (P) after m number of months for purchasing a car from the local dealership. – What is the slope of the line represented by this equation? – What does the slope represent in this situation? – What is the y-intercept of the line? – What does the y-intercept represent in this situation? • Practice – WB 3-5 # 4, 8, 13, 14, 21, 27, 28, 36, 45, 46 • EXIT

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# 3-5 (part 2) Open Response