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MATH 91: BEGINNING ALGEBRA Rev: Winter 2010 Names: Hour: Worksheet on Slope-Intercept Form Overview: The goal of this worksheet is to help you review the concepts of intercepts and slope as well as begin recognizing connections between the numbers in a linear equation and the features on the graph. Part I – Review of Intercepts and Slope 1. The following tasks help you review the major ideas and procedures involving intercepts and slope. a) Use the graph to find the intercepts and slope of line L. L M 5 b) Do the same tasks for line M. 5 -5 -5 c) Now use the equation 5 x 3 y 12 to find the intercepts and calculate the slope from those points. Then graph your line. 5 d) Do the same tasks for y 2 x 1. 7 5 -5 -5 Page 1 of 4 Part II – Slope-Intercept Form for Graphing Linear Equations 2. The next step is to use slopes and intercepts to create graphs of lines. The basic idea is that you put a dot on the grid at any point you are given, then use the slope to “walk” from there rise to new points using the idea for slope. Use the following information to graph lines on run the given grid. L: slope = 3 , x-intercept: (–2, 0) 4 M: slope = –2, point: (1, 0) N: y-intercept: (0, 6), slope = 5 5 -5 -5 2 5 3. Given a slope and y-intercept, we can build an equation for the line quite easily. We use what is called slope-intercept form: y mx b , where m is the slope, and b is the yintercept. Use the data for the lines you graphed in task 2 (reproduced below) to write the equations for those lines. 3 L: slope = , x-intercept: (–2, 0) 4 M: slope = –2, point: (1, 0) N: y-intercept: (0, 6), slope = 2 5 4. Slope-intercept form ( y mx b ) is the easiest form of a linear equation to use for graphing. You simply read off the y-intercept, plot that point, and then move to other points using the slope. Practice this method for graphing the following equations. 4 a) y x 3 7 5 b) 5 x 2 y 7 (convert to slopeintercept form first, then graph) 5 -5 -5 Page 2 of 4 Part III – Special Situations Involving Lines The following table will help you organize information about the most important “special cases” involving linear equations and their graphs. Horizontal Lines Graph looks like: y Vertical Lines Graph looks like: y x x Equation looks like: _________________ Equation looks like: _________________ Slope is always ____________ (m = ____ ) because Slope is always ____________ (m = ____ ) because Parallel Lines Graph looks like: Perpendicular Lines Graph looks like: y y x x What I should notice about the two lines is: What I should notice about the two lines is: ___________________________________ ___________________________________ The slope for the first line (m1) is always ___________________________________ the slope for the second line (m2). In symbols: The slope for the first line (m1) is always ___________________________________ the slope for the second line (m2). In symbols: Page 3 of 4 Extra grids to use for graphing: 5 5 5 -5 5 -5 -5 -5 5 5 5 -5 5 -5 -5 -5 5 5 5 -5 -5 5 -5 -5 Page 4 of 4