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## CRCT Review

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**CRCT Review**• Three runners are in a race. If they all finish at different times, in how many ways can they finish the race in first, second and third place? a. 3 b. 6 c. 9 d. 12 • Which of the following is the set of integers greater than -5 and less than 2? a. {-5, -4, -3, -2, -1, 0, 1, 2} b. {-5, -4, -3, -2, -2, -1, 1, 2} c. {-4, -3, -2, -1, 0, 1} d. {-4, -3, -2, -1, 1} • If Nora rolls a number cube with faces numbered 1 through 6 and spins a spinner with 8 equal sections labeled A through H, what is the probability that the number cube will show a number greater than 1 and the spinner will land on a vowel? a. b. c. d.**Parallel Lines**• Two lines with the same slope are said to be parallel lines. If you graph them they will never intersect. • We can decide algebraically if two lines are parallel by finding the slope of each line and seeing if the slopes are equal to each other. • We can find the equation of a line parallel to a given line and going through a given point by: • a) first finding the slope m of the given line; • b.) finding the equation of the line through the given point with slope m.**Testing if Lines are Parallel**Are the lines parallel? Find the slope of The slope m = -4 The slope m = -4 Find the slope of Since the slopes are equal the lines are parallel.**Practice Testing if Lines are Parallel**Are the lines parallel? Since the slopes are different the lines are not parallel. parallel? Are the lines Since the slopes are equal the lines are parallel.**Parallel Equations**• Parallel lines have the same slope • Given: y = 3x + 6, write an equation parallel that passes through (4, 7) m = 3. Use y = mx + b to find the other equation. Substitute m =3; x = 4; y = 7 to find b. 7 = 3(4) + b 7 = 12 + b -12 -12 -5 = b The new equation with point (4,7) is: y = 3x - 5**Testing if Lines Are Perpendicular**Since the slopes are negative reciprocals of each other the lines are perpendicular.**Practice Testing if Lines Are Perpendicular**Since the slopes are not negative reciprocals of each other (their product is not -1) the lines are not perpendicular Since the slopes are negative reciprocals of each other (their product is -1) the lines are perpendicular.**Perpendicular Equations**• Perpendicular lines have the “opposite reciprocal” slope. • Given: y = -3x + 1; write an equation perpendicular passing through (6, -1) So, m = 1/3. Use y = mx + b to find the other equation. Substitute m = 1/3; x = 6; y = -1 to find b. -1 = 1/3(6) + b -1 = 6/3 + b -1 = 2 + b -2 -2 -3= b The new equation with point (6,-1) is: y = 1/3x - 3