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Name: _______________________________ Class: ______ Math 10C Linear Relations, Equations and Graphs Practice Test FORMULAS: m= 𝑦2 −𝑦1 Multiple Choice: 1. 3. 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 ) Ax + By + C = 0 Circle the letter that corresponds with the correct or best answer. 2 marks each - Show your work to get full marks. 2 The point (−4, 0) is on a line which has a slope of − 5. The next point with integer coordinates on the line to the right of this point is A. B. C. D. 2. y = mx + b 𝑥2 −𝑥1 (−9, −2) (−9, 2) (1, −2) (−2, −5) The slope of the line segment joining A(5, −1) and F(3, 7) is A. B. −3 −4 C. − D. − 1 3 1 4 A line is parallel to the x-axis and passes through the point (−6, 10). The equation of the line is A. B. C. D. x = 10 x = −6 y = 10 y = −6 4. The slope-point form of the equation of the line passing through the point (−3, 5) with a slope of 5. 3 2 is 3 A. y + 5 = 2 (x – 3) B. y – 3 = 2 (x + 5) C. y – 5 = 2 (x + 3) D. y + 3 = 2 (x – 5) 3 3 3 The equations of 4 straight lines are given below: i) 7x – y = 0 ii) 7x + y – 6 = 0 iii) x – 7y + 4 = 0 iv) x + 7y – 2 = 0 Which pairs of lines are perpendicular? A. B. C. D. 6. i and ii i and iv both i and iv and ii and iii both i and ii and iii and iv Which of the following linear relations is not equivalent to the other three? A. B. C. D. 1 y – 4 = − 3 (x + 6) x + 3y + 2 = 0 the line passing through (0, 2) and (6, 0) 1 y = −3 x + 2 Written Response: Show your work for full marks. 1. Identify the slope of each line segment graphed below. 1 2. The slope of a line is 2 . The line passes through the point (4, -1). Name the coordinates of two other points on the line. 3. a) On the grid given below, graph a line that passes through the point (-2, -1) and is parallel to y the y-axis. b) What is the slope of the line? x c) Write the equation of the line. 4. Write the equation of a line in slope y-intercept form if it passes through (0,-1) and is perpendicular to the line y = 4x – 2. 𝟒 5. a) Given the line with the equation y – 3 = − 𝟕(x + 2), identify: i) slope ii) coordinates of a point b) Graph the line on the grid provided. c) Write the equation in slope y-intercept form. d) Write the equation in general form. y x 6. Without using technology, graph the line 2x – y + 6 = 0 on the grid provided. Show your work below. y x 7. Write the equation of a line, in general form, if it is perpendicular to the line x + 3y = 0 and it has the same y-intercept as the line 2x + 3y – 1 = 0. 8. A boat rental company charges their customers a flat fee plus a rate per hour for renting a boat. If a customer rents a boat for 5 hours, their total cost is $140. If a boat is rented for 8 hours, the total cost is $200. a) Identify the coordinates of 2 points which lie on the graph of this linear relationship. b) Determine an equation, in all 3 forms, to represent the information. c) Explain what the slope and the y-intercept represent in this situation. d) How much will it cost to rent a boat for 2 hours?