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Algebra SOL Review: Slope and Variation I. Calculating Slope given two points or given a graph: If given two ordered pairs, use the formula m y2 y1 . x2 x1 rise . run Horizontal lines have a slope of ____________________. Vertical lines have a ______________________ slope. Parallel lines have the _________________ slope. Slopes of perpendicular lines have a product of __________. If given a graph, count Determine the slope of the line that passes through the points (12, 6) and (12, -5). Determine the slope of the line pictured below. Look at the lines on the graph to the right. Which has a positive slope? Which has a negative slope? Which has a slope of 0? Which has an undefined slope? II. Graphing a line given a point and the slope: Plot the given point. Use the slope to find a second point. Connect to graph the line. Graph the line passing through (3, 4) with slope III. Graphing Equations in Slope-Intercept Form y = mx + b Start by plotting a point on the y-intercept (b ). Use your slope (m ) to rise and run to another point on the line. Connect the two points you plotted. Graph: 2 y x 8 5 Write an equation for the graph. 2 . 3 IV. Graphing Equations in Standard Form: Calculate the x - intercept and y - intercept. Plot these two points and connect to graph the line. Graph the equation 3x – 8y = -24. The graph to the right is best represented by which equation? [A] 5x + 4y = 20 [B] 5x – 4y = 20 [C] 4x + 5y = 20 [D] 4x – 5y = 20 VI. Writing an equation given a point and the slope: Use ( x1 , y1 ) and m values given to substitute into y y1 m( x x1 ) . Solve for y. Write an equation for the line that goes through the point (-1, 5) and has a slope of –2. Check to see if your equation makes sense by graphing as we did in II. Write an equation for the line that goes through the point (4, 5) and 3 has a slope of . 4 Check to see if your equation makes sense by graphing as we did in II. V. Writing an equation given 2 points: Calculate slope using the formula m y2 y1 x2 x1 . Use one of your points as ( x1 , y1 ) and m value given to substitute into y y1 m( x x1 ) . Solve for y. Write an equation for the line that passes through the points (-3, 6) and (5, 6). VI. Check to see if your equation makes sense by plotting the two ordered pairs. Variation: Direct Variation: y = kx or k y x The graph would be a straight line passing through the origin. “y” varies directly as “x ” From the table, determine if y varies directly as x. If so, write the equation describing the variation. x -2 -1 3 5 y 6 3 -9 -15 At a given time and place, the height of an object varies directly as the length of its shadow. If a flagpole 6 meters high casts a shadow 10 meters long, find the height of a building that casts a shadow 45 meters long. Inverse Variation: x y k is the form of an inverse variation equation, where k is the constant As input values increase, output values decrease and vice versa Graphs of Inverse Variations are not linear In the table below, determine the equation of variation and identify if it is a direct or inverse variation. X 5 Y 8 A. B. C. D. 40 2 10 1 20 -4 y = 1.6x, Direct y=1.6x, Inverse xy 40 , Direct xy 40 , Inverse VII. Solving Systems of Linear Inequalities: Graph both linear inequalities on the same coordinate grid a. Easier if put in y = mx + b b. Shade the “true side” of both lines c. Line is solid if or d. Line is dotted if or The solution includes the entire region that is shared by both inequalities. Solve the system by graphing. y x 3 y x 6