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LINEAR RELATIONS REVIEW

LINEAR RELATIONS REVIEW. Grade 9 Academic Math. Important Terms…. Linear relationship: first differences will be same; produces a straight line when graphed; degree of equation is 1

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LINEAR RELATIONS REVIEW

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  1. LINEAR RELATIONS REVIEW Grade 9 Academic Math

  2. Important Terms… • Linear relationship: first differences will be same; produces a straight line when graphed; degree of equation is 1 • Non-Linear relationship: first differences will not be same; produces a curve when graphed; degree of equation is not 1 • Table of values: is a way of organizing coordinates of the graph; contains X and Y values • First Differences: subtracting the Y - value below the number in the Y column from the number above it; finite differences • Independent variable: the value that determines the dependent variable; X – value

  3. Important Terms… • Dependent variable: value depends on the value of independent variable; Y - value • Direct Variation: doesn’t have flat/initial rate; passes through the origin (0,0) • Partial Variation: have a flat/initial rate; doesn’t passes through the origin (0,0) • Slope: steepness of line; rise over run • X-intercept: set Y as zero; (X,0); on the x - axis • Y-intercept: set X as zero; (0,Y); on the y - axis

  4. Slope and y-intercept form

  5. Standard Form Ax + By + C = 0 • A, B and C = integers • Any A, B and C = 0, but not A and B at the same time • A is positive • No fractions

  6. Finding Slope… • Find first differences; dividing delta y by the delta x • Counting the rise and the run; in lowest possible fractions; as • Using the formula

  7. Finding X and Y intercepts… • For x – intercept: set Y as zero and solve the equation of line; on the x - axis • For y – intercept: set X as zero and solve the equation of line; on the y - axis

  8. Finding the Equation of a Line… • Slope and a point given: • Plug the value of slope and the point in the linear equation. • Solve for y – intercept (b in linear equation). • Two points given: • Find the slope of line using slope formula. • Substitute the slope and a point in the linear equation. • Solve for y – intercept (b in linear equation).

  9. Special Cases of Lines… Special cases include: • Parallel Lines • Perpendicular Lines • Intersecting Lines • Horizontal Lines • Vertical Lines

  10. Parallel Lines… • Slopes of parallel lines are same • Different y - intercepts • Lines having the same slopes are parallel

  11. Perpendicular Lines… • Slopes of perpendicular lines are negative reciprocal • Lines have slopes that are negative reciprocal, they are perpendicular lines

  12. Intersecting Lines… • Slopes of lines are different from each other • Different y – intercepts • All lines having different slopes intersect each other once on the graph

  13. Horizontal Lines… • Graph: horizontal line, parallel to x - axis • Equation:y = b; as y coordinates stays the same • Slope: m = 0; no rise

  14. Vertical Lines… • Graph: vertical line, parallel to y – axis • Equation: x = a; where a = x – intercept • Slope: m = undefined, no run

  15. Point of Intersection… • Graphing the lines: finding the coordinates of point where lines intersect • Algebraic method, using substitution or elimination: • Balance the equations; let one equation equal the other • Collect x terms on one side and solve for x • Substitute x value in an equation and find y • Put the values in an ordered pair

  16. Rearranging the Equation of Line Equation: ax + by = c • Change into Ax + By + C = 0 (standard form) • Change into y = mx + b (slope and y – intercept) • ax + by = c and Ax + By + C = 0 can be changed into y = mx + b, meaning a linear relation and graph will have a straight line

  17. GAME TIME !!!

  18. Alvi, Ali, Aniqa, Cody, Brendan, Nathalia Adesh, Imauni, Mirabelle, Stella, Shehzad Jacob, Etornam, Hajr, Jude, Wardah, Tyrone Nick, Amber, Rachel, Tina, Edward, Shaquan Remi, Everett, Khadijah, Mahnoor, Vaidehi Groups…

  19. Question #1 Which of the following can be used to find the slope of a line? i) ii) iii) • i) only • iii) only • i), ii) only • i), ii) and iii) Answer : i), ii) and iii)

  20. Question #2 Suppose the slope of a line was negative. Select the true statement. • The line is not very steep • The line falls to the right • The line has no x – intercept • The line is very steep Answer : The line falls to the right

  21. Question #3 The student council sells lollipops for 10 cents each. They pay 4 cents for each lollipop and spend $10 to advertise the sale. P represents the student council’s profit, in dollars, and n represents the number of lollipops sold. Which equation represent the profit? • P = 0.06n – 10 • P = 0.06n + 10 • P = 10n + 0.06 • P = 10 + 0.04n Answer : P = 0.06n – 10

  22. Question #4 Which of the following lines has the greatest slope? • 2x + 3y – 10 = 0 • 5x – 3y +15 = 0 • x + 2y – 8 = 0 • x – y + 7 = 0 Answer : 5x – 3y +15 = 0

  23. Question #5 The cost, C, in dollars to print n leaflets is given by the formula C = 35 + 0.03n. What is the cost of printing 900 leaflets? • $27.00 • $35.00 • $37.70 • $62.00 Answer : $62.00

  24. Question #6 The line y = kx + 6 is perpendicular to the line y = ¾ x + 10. Select the value of k. • – 4/3 • - ¾ • -3 • ¾ Answer : - 4/3

  25. Question #7 What are the coordinates of the point of intersection of the lines y = -x + 1 and x = 3? • (2, 3) • (3, 2) • (3, -2) • (-2, 3) Answer : (3, -2)

  26. Question #8 Sam charges a $5 base fee plus $20/h to fix jewellery. In this relationship, what is the dependent variable? • The $5 base fee • The number of hours • The cost • The jewellery Answer : the cost

  27. Question #9 Four points, A(-3, 4); B(-5, -4); C(2, -2) and D(3, 3) lie on an xy- plane and are joined by line segments. Which line segment has a negative slope? • BA • BC • CD • AD Answer : AD

  28. Question #10 Donna has correctly drawn a line on an xy-plane. Her plane is parallel to the line y = x + 1 and has the same y-intercept as the line y = 2x + 6. Which of the following equations represents the line that Donna had drawn? • y = x + 3 • y = -x + 6 • y = x + 6 • y = -x + 3 Answer : y = x +6

  29. Question #11 The points A(-3, -4) and B(6, 2) are placed on an xy-plane. Which statement about the line through AB is not true? • Its x-intercept is 3 • Its slope is positive • Its y-intercept is -2 • Passes through (4, 9) Answer : passes through (4, 9)

  30. Question #12 What is the slope of a line that is perpendicular to 3 – x + 4y = 0? Answer : slope = -4

  31. Question #13 What is the equation of the line that passes through the point (2, 0) and is parallel to the line y = -3x + 4? • y = 3x + 2 • y = 3x + 6 • y = -3x + 2 • y = -3x + 6 Answer : y = -3x + 6

  32. Question #14 Temira needs to rent a car. She considers the following price equations, where C is the total cost, in dollars, and n is the number of days. Which company should she choose if she is planning to rent the car for at least 10 days. • Rentway • Cheapie’s Rental • Cars Cars • Drive Away Answer : Drive Away

  33. Question #15 What is the equation of a line passing through the points (2, 5) and (4, 11)? • y = x – 3 • y = 2x - 1 • y = 3x - 1 • y = 4x – 3 Answer : y = 3x - 1

  34. Question #16 Scientists find that the height of a person, h, in centimeters, is related to the length of the person’s femur bone, f, in centimeters, according to the following formula: h = 69.09 + 2.24f. According to the formula, what is the height of a person with a femur bone of 48.6 cm in length? • 109 cm • 178 cm • 186 cm • 347 cm Answer : 178 cm

  35. Question #17 Determine if the following pair of lines are parallel, perpendicular or neither. Line 1: M (-2, -8); N (3, 5) Line 2: R (0, -9); S (5, 4) Answer : parallel

  36. Question #18 Lori downloads music from Music site, which charges a monthly membership fee plus and an amount for each song downloaded. In February, she was charged $25.30 for 38 songs downloaded. In March, she was charged $23.60 for 21 songs downloaded. Determine the equation of the relationship between numbers of downloads and her monthly bills. Answer : y = 1/10x + 21.50

  37. Question #19 The slope of the line y = 3 is: • 1 • 0 • 3 • Undefined Answer : 0

  38. Question #20 The slope of the line x = 7 is: • 1 • 7 • 0 • Undefined Answer : undefined

  39. Question #21 Classify each relation as a direct variation, partial variation or neither. • d = 45t • y = 2x + 3 • y = 10x • d = 45t + 12

  40. Question #22 Find the equation of the line perpendicular to 3x + y – 2 = 0 and having the same x-intercept as the line 5x – 9y + 45 = 0. Write the equation in standard form. Answer : y = 1/3x + 3

  41. Question #23 To purchase a fishing license, it costs $25/year plus a one-time $5 fee for processing the application. In this relationship, what is the independent variable? • The $5 fee for processing • The number of years • The cost • The $25/year fee Answer : the number of years

  42. Question #24 Bob is the editor of the school yearbook. He is in charge of collecting money from students for yearbooks. He collects $35 per student. The money he collects depends on the number of students who buy yearbooks. • What are the two variables? • Is this a direct or partial variation?

  43. Question #25 Find the point of intersection for the following system algebraically. y = -2x – 8 y = - 2/3x – 4 Answer : P.O.I is (-3, -2)

  44. Question #26 Find the equation of a line parallel to 2x + 5y = 1, with the same y-intercept as x – 4y = 8. Answer : y = -2/5x - 2

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