PRACTICE TEST: Chapter 6 - Linear Equations

Transcription

1 Class: Date: PRACTICE TEST: Chapter 6 - Linear Equations Multiple Choice Identify the choice that best completes the statement or answers the question 1 Which of these line segments are parallel? a CD and EF c AB and CD b EF and GH d AB and EF 2 Determine the slope of the line that is perpendicular to this line segment a c 1 b d 1 Determine the slope of a line that is perpendicular to the line through W( 9, ) and X(6, 10) a 1 1 b 1 1 c 1 d 1 1 1

2 4 Determine the slope of the line that is parallel to this line segment a c b d Determine the slope of a line that is parallel to the line through L( 6, ) and K(12, 9) a 2 c 2 b 2 d 2 6 A line has x-intercept 4 and y-intercept Determine the slope of a line perpendicular to this line a 4 c 4 b 4 d 4 A line passes through J( 10, 10) and K(, 9) Determine the coordinates of L so that line JL is perpendicular to line JK a L(2, 9) c L(1, 19) b L( 19, 1) d L(9, 2) 8 A line passes through D(, ) and N(12, 4) Determine the coordinates of two points on a line parallel to DN a (6, 10) and (24, 8) c ( 10, 6) and (24, 8) b ( 10, 24) and (6, 8) d ( 10, 6) and ( 8, 24) 9 Write an equation for the graph of a linear function that has slope 1 and y-intercept a y = x 1 c y = 1 x + b y = 1 x d y = x 1 2

3 10 Write an equation for the graph of a linear function that has slope 1 and y-intercept 8 a y = x + 8 c y = 8x + 1 b y = 8x + 1 d y = x 8 11 Which graph represents the equation y = 2 x + 1? a c b d 12 Which equations represent parallel lines? a y = 8x + 8, y = x + 8 c y = 8x, y = 14x + 14 b y = 14x, y = x + 8 d y = x + 14, y = x Which equations represent perpendicular lines? a y = 6x, y = 6x + c y = 11x, y = 11x + 1 b y = x + 11, y = 1 x + 6 d y = 1 x + 6, y = 6x + 6 6

4 14 Write an equation to describe this graph a y = 1 x 1 c y = 1 x 1 b y = 1 x + 1 d y = 1 x Determine the slope and y-intercept of this graph a slope: 4 ; y-intercept: 1 c slope: ; y-intercept: 1 4 b slope: 1; y-intercept: 4 d slope: ; y-intercept: 1 4 4

5 16 Describe the graph of the linear function with this equation: y + = 1 (x 2) a The graph is a line through ( 2, ) with slope 1 b The graph is a line through (2, ) with slope 1 c The graph is a line through (2, ) with slope 1 d The graph is a line through ( 2, ) with slope 1 1 Write an equation for the graph of a linear function that has slope 8 and passes through R(4, ) a y + = 8(x 4) b y + = 8(x 4) c y + = 1 (x 4) 8 d y = 8(x + 4) 18 Write an equation for the graph of a linear function that has slope 2 and passes through S( 4, ) a y + = 2 (x 4) b y = 2 (x + 4) c y = (x + 4) 2 d y = 2 (x + 4) 19 Write this equation in slope-intercept form: y = 1 (x + 2) a y = 1 x + 1 c y = x + 1 b y = x + 1 d y = 1 x Write this equation in slope-intercept form: y = 2 (x + 10) a y = 2 x + 1 c y = x + 1 b y = 2 x + 1 d y = 1 x Determine the y-intercept of the graph of this equation: y = 4(x + ) a c 2 b 2 d 20

6 22 Which graph represents the equation y + 1 = (x + )? 4 a c b d 2 Write an equation in slope-point form for the line that passes through A( 2, 4) and B( 9, 6) a y 6 = 2 (x + 2) c y 4 = 2 (x + 2) b y + 4 = 2 (x 2) d y + 6 = 2 (x 2) 24 Write an equation in slope-point form for the line that passes through A(1, 4) and B(6, 8) a y + 8 = 4 (x 1) c y 4 = 4 (x 1) b y + 4 = 4 (x 1) d y 8 = 4 (x + 1) 6

7 2 Write an equation in slope-point form for this line a y 2 = 1 2 (x 2) c y 2 = 1 (x 2) 2 b y + 2 = 1 2 (x + 2) d y + 2 = 1 (x + 2) 2 26 Write an equation for the line that passes through T(, ) and is parallel to the line y = x 10 a y + = 1 (x ) c y = 1 (x + ) b y + = (x ) d y = (x + ) 2 Write an equation for the line that passes through U(, ) and is perpendicular to the line y = 1 x 9 a y + = 1 (x + ) c y + = (x ) b y = (x + ) d y + = (x ) 28 Write this equation in general form: y = x + a x + y = 0 c x y + = 0 b x + y + = 0 d x y = 0 29 Write this equation in general form: y = 2 x + 8 a x + 2y 16 = 0 c x + 2y 8 = 0 b x 2y + 8 = 0 d x 2y 16 = 0 0 Determine the slope of the line with this equation: x + y + = 0 a c b d

8 1 Write this equation in slope-intercept form: 10x + y 4 = 0 a y = 10 x + 4 c y = 10 x 4 b y = 10 x + 4 d y = 10 x 4 2 Which graph represents the equation 4x 6y 12 = 0? a c b d A line has x-intercept 9 and y-intercept Determine the equation of the line in general form a x + 9y 2 = 0 c x 9y + 2 = 0 b x 9y 2 = 0 d x + 9y + 2 = 0 4 For the function f x= x + 8, determine f( 2) a b 2 c 14 d For the function f x= x + 8, determine x when f x= 2 a 8 b 6 c 11 d 11 8

9 6 For the function g x= 2x 9, determine g(4) a 22 b 22 c 6 d 62 For the function g x= 2x 9, determine x when g x= 1 a b 12 c 9 d 12 Short Answer 8 Are these two line segments parallel, perpendicular, or neither? 9 Graph the line with y-intercept and slope 2 40 Write an equation for the line that passes through E(, ) and F(2, 10) Write the equation in slope-point form and in slope-intercept form 41 Write this equation in general form: y = 9 4 x 42 Determine the slope of the line of this equation: 9x + y 1 = 0 9

10 4 What is f(-)? 44 What is f(4)? 10

11 Problem 4 Reggie says FGHJ is a parallelogram Ann says FGHJ is a rectangle Who is correct? Justify your answer 46 In Canada, the number of girls playing organized ice hockey from January 1990 to January 2010 increased by approximately 4162 girls per year In January 2000, there were approximately girls playing organized ice hockey a) Write an equation in slope-point form to represent the number of girls, n, playing organized ice hockey as a function of the number of years, t, after 1990 b) Use the equation in part a to estimate the number of girls playing organized ice hockey in January Write an equation for the line that passes through B( 1, ) and is: a) parallel to the line y = x b) perpendicular to the line y = x 48 Determine the slope of a line that is perpendicular to the line with this equation: 8x + y + = 0 11

12 PRACTICE TEST: Chapter 6 - Linear Equations Answer Section MULTIPLE CHOICE 1 D 2 D D 4 C C 6 A D 8 C 9 B 10 A 11 B 12 D 1 B 14 A 1 A 16 B 1 B 18 D 19 A 20 B 21 C 22 C 2 C 24 C 2 A 26 D 2 C 28 C 29 A 0 A 1 B 2 A C 4 C C 6 A A 1

13 SHORT ANSWER 8 Neither 9 40 y + = 1 (x + ) y = 1 x + 16 or y 10 = 1 (x 2) y = 1 x x 4y 28 = Horizontal intercept: Vertical intercept: 2 44 Rate of change: 1; vertical intercept: 2 2

14 PROBLEM 4 A parallelogram has opposite sides equal To check whether FGHJ is a parallelogram, determine whether opposite sides are parallel Write the coordinates of the vertices: F(, 2), G( 1,2), H(4,1), J(2, ), Slope of GH = y y 2 1 x 2 x Slope of GH = 4 ( 1) Slope of GH = 1 The slope of GH is 1 Slope of FJ = y y 2 1 x 2 x 1 ( 2) Slope of FJ = 2 ( ) Slope of FJ = 1 The slope of FJ is 1 Slope of HJ = y 2 y 1 x 2 x 1 Slope of HJ = ( ) Slope of HJ = 4 2 The slope of HJ is 2 Slope of GF = y 2 y 1 x 2 x 1 Slope of GF = ( 2) 2 ( 1) Slope of GF = 4 2 The slope of GF is 2 The slopes of opposite sides are equal, so FGHJ is a parallelogram A rectangle has angles that are right angles To check whether FGHJ is a rectangle, determine whether two intersecting sides are perpendicular Determine whether GF is perpendicular to GH

15 The slope of GF is 2 The slope of GH is 1 Since the slopes of GF and GH are not negative reciprocals, GF and GH are not perpendicular This means that FGH is not a right angle and that FGHJ is not a rectangle So, Reggie is correct 46 a) The increase in girls playing organized ice hockey is 4162 girls per year This is the slope of a graph of this function The year 2000 is = 10 years after 1990 So, an ordered pair that satisfies this function is: (10, 4 400) Use the slope-point form of the equation of a linear function: y y 1 = m(x x 1 ) Replace y with n, and replace x with t n n 1 = m(t t 1 ) Substitute m = 4162, n 1 = 4 400, and t 1 = 10 into the equation n = 4162(t 10) b) The year 2009 is 19 years after 1990 Substitute t = 19 in the equation: n = 4162(t 10) n = 4162(19 10) n = 4162(9) n = 48 n = There were approximately girls playing organized ice hockey in January

16 4 Sketch the line with equation: y = x, and mark a point at B( 1, ) Compare the equation: y = x with the equation: y = mx + b The slope of the line is a) Any line parallel to y = x has slope The required line passes through B( 1, ) Use: y y 1 = m(x x 1 ) Substitute y 1 =, x 1 = 1, and m = y = [x ( 1)] y = (x + 1) The line that is parallel to the line y = x and passes through B( 1, ) has equation: y = (x + 1) b) Any line perpendicular to y = x has a slope that is the negative reciprocal of ; that is, its slope is The required line passes through B( 1, ) Use: y y 1 = m(x x 1 ) Substitute y 1 =, x 1 = 1, and m =

17 y = [x ( 1)] y = (x + 1) The line that is perpendicular to the line y = x and passes through B( 1, ) has equation: y = (x + 1) 48 Rewrite the equation in slope-intercept form 8x + y + = 0 y + = 8x y = 8x y = 8 x From the equation, the slope of the line is 8 Any line perpendicular to 8x + y + = 0 has a slope that is the negative reciprocal of 8 ; that is, its slope is 8 6