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Lesson 3.2 Revisiting Slope Notes Slope - ____________ of the vertical change to the corresponding horizontal change. In other words it is the ________________________________. Given points (x1, y1) and (x2, y2), m = y2 – y1 = change in y x2 – x1 change in x Try it! Find the slope of a line that goes through (6, 9) and (-2, 5) Slope-Intercept Form y = mx + b Try it! The slope of a line is 2/3. The y-intercept is -5. Write the equation of the line and name another point on the line. Example Write the equation of the line that passes through the points (3,2) and (-9, 6) Your Turn! Write the equation of the line that has a slope of -1/4 and goes through the point (8, -9). Example Graph y = (2/3)x + 3 Remember: You can always make a table! Your Turn! Graph 2x + y = -2. THINK! Standard Form of a Linear Equation Ax + By = C where A, B, and C are real numbers. This is useful to find the X-Intercept and the Y-Intercept. Remember** The x-intercept is the ordered pair ___________ The y-intercept is the ordered pair ___________ The equation of a vertical line is __________. The equation of a horizontal line is __________. Example Graph 3x + 2y = 12. Then change the equation to slope-intercept form and check to make sure it is the same. Your Turn! Graph -2x + 5y = -10. Then change the equation to slope-intercept form and check to make sure it is the same. Parallel Lines If lines are parallel, then their slopes are ______________ Perpendicular Lines If lines are perpendicular, then their slopes are _______________________________________________________________. *What if they were just negatives of each other? For example: 2/3 and -2/3. What’s their relationship? Example: Given the equation y = ¾x + 2, write and graph the equation of the line that goes through a. is parallel and goes through (0, 4) b. is perpendicular and goes through (6, 1) Your Turn! Write an equation for each line. Then graph the lines. a. through (-1, 3) and perpendicular to the line -5x + y = – 3 b. through (2,1) and parallel to the line y = 2/3x + 8 c. vertical and through (5, -3)