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AIMS Math Prep Linear Equations Graphing March 30, 2009 Monday find the y-intercept, Period 1 To locate where the line crosses the vertical (y) axis. e.g. -2 1. 5. Find the y-intercept for each graph. 2. 3. 4. 6. 7. 8. Check out http://www.ltcconline.net/greenl/java/BasicAlgebra/LineGraph/LineGraph.htm find the y-intercept, Period 1 To locate where the line ANSWERS 1. crosses the vertical (y) axis. e.g. -2 Find the y-intercept for each graph. 1 2. 3. 1 4. 4 -2 5. 6. -1 7. -3 Check out 2 8. -1 http://www.ltcconline.net/greenl/java/BasicAlgebra/LineGraph/LineGraph.htm Period 2 To find the slope, locate a point on the left and count the number you spaces you go up (+) or down (-) to get to the next point. -2 = -1 4 2 1. 5. Find the slope for each graph. 2. 3. 4. 6. 7. 8. Check out http://www.ltcconline.net/greenl/java/BasicAlgebra/LineGraph/LineGraph.htm Period 2 ANSWERS To find the slope, locate a point on the left and count the number you spaces you go up (+) or down (-) to get to the next point. -2 = -1 4 2 1. Find the slope for each graph. -1 5. 2. 3 2 6. 4 7. 0 Check out 3. 4. -2 0 8. -1 -1 5 http://www.ltcconline.net/greenl/java/BasicAlgebra/LineGraph/LineGraph.htm the equation of the Period 3 Write line in slope intercept form y = (slope)x + y-intercept e.g. y = ½ x - 2 Find the equation of the line for each graph. 1. 2. 3. 4. 5. 6. 7. 8. Check out http://www.ltcconline.net/greenl/java/BasicAlgebra/LineGraph/LineGraph.htm Period 3 Write the equation of the line in slope intercept form y = (slope)x + y-intercept ANSWERS e.g. y = ½ x - 2 1. Find the equation of the line for each graph. y x 1 5. y 4x 1 2. 3. y 3 x 1 2 6. y 2 x 4 7. y 3 Check out y2 4. y x 2 8. 1 y x 1 5 http://www.ltcconline.net/greenl/java/BasicAlgebra/LineGraph/LineGraph.htm Period 4 Write the equation of each line. Vertical lines are in the form x = ___ and horizontal lines are in the form y = __ with the __ being the point where the line crosses. 1. 2. 3. 4. 5. 6. Period 4 ANSWERS Write the equation of each line and its slope. Vertical lines are in the form x = ___ and horizontal lines are in the form y = __ with the __ being the point where the line crosses. 1. 4. y=1 Slope = 0 y = -4 Slope = 0 2. 5. y = -3 Slope = 0 x=8 Slope is undefined 3. x = -1 Slope is undefined 6. x = -4 Slope is undefined Period 5 Determine if the lines are parallel (equal slope), perpendicular (form right (90°) angles with negative inverse slopes (opposite signs & flipped)), or neither. 1. 2. 3. 4. y = ½ x + 5 y = -2x + 8 5. 4y = 8x – 5 3y = 6x + 2 6. 3y + 9x = 13 2y + 6x = 4 Period 5 ANSWERS Determine if the lines are parallel (equal slope), perpendicular (form right (90°) angles with negative inverse slopes (opposite signs & flipped)), or neither. Parallel slope = ½ 1. Neither Slopes are 2/3 & -1 2. 4. y = ½ x + 5 Perpendicular 5. 4y = 8x – 5 Parallel y = -2x + 8 Slopes: ½ & -2 3y = 6x + 2 slopes = 2 Perpendicular 3. slope -2 & ½ 6. 3y + 9x = 13 2y + 6x = 4 Parallel Slopes = -3 Period 6 Find the solution to the system of equations graphed. (locate the point of intersection) 1. 2. 3. 4. 5. 6. Period 6 ANSWERS Find the solution to the system of equations graphed. (locate the point of intersection) 1. 2. 3. (3, 1) (-3, -3) 4. No solution 5. (-6, -2) 6. (4, 6) (0, 2)