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MPM1D Exam Review 1. Chapter 6 – Linear Relations Match each linear equation with the graph that best suits it. 2. Identify the slope and y-intercept for each of the relations shown below. Then, write the equation of each line. iv) i) iii) ii) 3. Convert the following to slope-intercept form. Identify the slope and y-intercept. 2 a) b) c) 7x 3y 19 2x 5y 8 0 y 3 x 1 5 4. Convert the following into standard form. a) 5. y 3x 7 b) y 3 11 x 5 2 c) y 7 2 x 4 3 Determine the x-intercepts, y-intercepts, and slope of each of the following. 5 a) b) c) 5x 4y 60 7x 6y 33 0 y x 14 2 6. Graph the following lines on the same grid. 4 a) y 8 b) x 7 c) y x 1 5 d) 3x 4y 12 e) y 3(x 6) 4 7. Determine whether the points A(2, -6), B(-3, 10) and C(-1, 1) are on the line 4x y 2 0 . 8. Find the equation of the line (in slope-intercept form) with a slope of 4 that passes through the 3 point (5, 7). 9. Find the equation of the line, in point-slope form, of the line that has a slope of through the point (-9, 12). 8 and passes 11 10. Determine the equation of the line that is perpendicular to the line 6x 10y 1 0 and has the same y-intercept as 3x y 1 . Express your equation in slope-intercept form. 11. Find the equation of the line that is parallel to the line 2x y 1 0 and passes through (8, -7). Express your equation in point-slope form. 12. Find the equation of the line perpendicular to 4x 3y 12 0 that has the same x-intercept as 3y 9x 18 0 . Express your answer in slope-intercept form. 13. Find the equation of the line the passes through: a) (3, -3) and (-3, 5) b) (5, 2) and (5, -3) c) (8, -5) and (2, 7) 14. Holly downloads music from a site called MyTunes, which chargers a monthly membership fee plus an amount for each song downloaded. A 3-month record of her site activity is shown below. a) Use two points from the table to determine an equation relating Holly’s monthly bill the number of songs she downloaded. b) Verify that the third point in the table satisfies your equation. Month January February March # of songs 54 38 21 Monthly Bill $26.90 $25.30 $23.60 15. Solve the following linear systems graphically. Check your solution. a) b) y 2x 5 and y 3x 5 x y 4 0 and x 2y 2 0 16. Majida needs to park her car downtown while she takes a course. She can buy a monthly pass for $82, or she can register for $10 and then pay $6 each day to park. Under which conditions should Majida buy the monthly pass? When should she go with the second plan? Chapter 6 Exam Review – Solutions 4 , 5 4 2 8 y-int: -2, y x 2 iii) slope: 0, y-int: 8, y 8 iv) slope: undefined, y-int: none, x 6 3a) y x , 5 5 5 2 8 7 19 7 19 2 13 2 13 slope: , y-int: b) y x , slope: , y-int: c) y x , slope: , y-int: 4a) 5 5 3 3 3 3 5 5 5 5 5 28 , y-int: -14, slope: b) x-int: -12, 3x y 7 0 b) 6x 10y 55 0 c) 2x 3y 13 0 5a) x-int: 5 2 11 5 33 7 b) y-int: 15, slope: c) x-int: , y-int: , slope: 6) 4 6 7 2 e) 4 41 8 7) A: yes, B: no, C: no 8) y x 9) y x 9 12 c) 3 3 11 5 3 3 10) y x 1 11) y 2x 8 7 12) y x 3 4 2 4 d) 13a) y x 3 3 b) x 5 c) y 2x 8 5 3 a) 14a) C 0.10n 21.50 15a) (2, -1) b) (2, 2) 16) If she is going to park more than 12 times, she should buy the monthly pass. If she parks fewer than 12 times, she should go with the second plan. If she parks exactly 12 times, then it doesn’t matter which plan she chooses. 1) (a) -> (iii), (b) -> (vi), (c) -> (iv), (d) -> (ii), (e) -> (i), (f) -> (v) 2i) slope: 2, y-int: 3, y 2x 3 ii) slope: