Find the coordinates of the labeled points. 1) 1) Identify the quadrant with the given condition. 4) The first coordinate is positive.

Transcription

1 M115 (Beginning Algebra) Chapter 3 Practice Test Name: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the coordinates of the labeled points. 1) 1) Determine the quadrant in which the point is located. 2) (-9, 18) 2) 3) (0, -2) 3) Identify the quadrant with the given condition. 4) The first coordinate is positive. 4) 5) The second coordinate is negative. 5) 6) The coordinates have the same sign. 6) 7) The first and second coordinates have the opposite signs. 7) Decide whether or not the ordered pair is a solution to the equation. 8) 4x - 5y = 18; (2, 2) 8) 9) 2x + 3y = 25; (5, 5) 9) 10) y = -3x; (1, -3) 10) 1

2 Show that the two ordered pairs are solutions to the given equation. Then use the graph of the two points to determine another solution. Answers may vary. 11) y = x - 2; (7, 5), (1, -1) 11) 12) x + 2y = 8; (6, 1), (-4, 6) 12) Graph the equation. 13) y = 4x ) 2

3 14) 2x - y = -6 14) Find the equation for the graph. 15) 15) 16) 16) 3

4 Find the coordinates of the y-intercept and the coordinates of all x-intercepts. 17) 17) 18) 18) Find the intercepts for the equation. 19) 2x + y = 2 19) 20) -5x + 5y = 10 20) 21) y = 17 21) 22) x = 4 22) 4

5 Find the x- and y-intercepts for the equation. Then graph the equation. 23) 16y - 4x = -8 23) 24) y = -2x+ 6 24) Graph the equation. 25) x - y = 6 25) 5

6 26) 8x = ) 27) y = 0 27) Write an equation for the graph. 28) 28) 6

7 29) 29) Identify the missing units for the given rate. 30) If a student drove 427 miles in 7 hours, his average rate was ) 31) If a construction worker layed 52 bricks along a 26-foot driveway border, his average rate was 2. 31) Solve the problem. 32) To the nearest dollar, the average tuition at a public four-year college was $3106 in 1998 and $3430 in Find, to the nearest dollar per year, the rate at which tuition was increasing. 32) 33) At 10:00 AM, Gavin rented a mountain bike. He returned the bike at 5:00 PM. He biked for 45.5 miles. He paid $42.00 for the rental. Find the rental rate, in dollars per mile. 33) 34) The following graph shows data for a recent train ride from New York to Toronto. At what rate did the train travel? 34) Time of Day (PM) 7

8 Make the most appropriate graph to match the situation. 35) Joe runs until he reaches the shore of a lake. He then rows a boat to the other side of the lake. He runs faster than he can row a boat. 35) 36) In the morning Brenda drives away from home at a steady speed. She stops for breakfast. She then continues to drive at a steady but faster speed. 36) Use the graph to solve the problem. 37) Find the rate of change in the temperature. 37) 8

9 38) Find the rate of change in Carlos's weight. 38) months since start of diet Find the slope of the line, or state that the slope is undefined if appropriate. 39) 39) 40) 40) 9

10 41) (3, 3) (3, -3) 41) 42) (-2, 1) (5, 1) 42) Find the slope of the line containing the given pair of points. If the slope is undefined, state so. 43) (3, 2) and (-5, 9) 43) 44) (-7, -9) and (-7, 3) 44) 45) (7, 7) and (-7, 7) 45) 46) (2, 2) and (8, 11) 46) Find the slope of the line. If the slope is undefined, state so. 47) x = -3 47) 48) y = 4 48) 10

11 Draw a line that has the given slope and y-intercept. 49) Slope - 1 ; y-intercept (0, 3) 49) 4 50) Slope 1 ; y-intercept (0, 4) 50) 3 Find the slope and the y-intercept of the line. 51) -6x + 8y = -8 51) 52) y = 15 4 x ) 53) y - 8 = 3 53) Find the slope-intercept equation for the line with the indicated slope and y-intercept. 54) Slope - 5 ; y-intercept (0, 4) 54) 8 55) Slope 4; y-intercept (0, 0) 55) 11

12 Graph the linear equation. 56) y = x ) Determine whether the pair of equations represents parallel lines. 57) 3x - 8y = 13 32x + 12y = 13 57) 58) 9x + 3y = 12 6x + 2y = 9 58) 59) y = 3x - 5 9x + 3y = 6 59) Write an equation in slope-intercept form of the line satisfying the given conditions. 60) Parallel to 4x - 7y = 29, y-intercept (0, -5) 60) 61) Perpendicular to 6x - 5y = 8 and the same y-intercept as 4x + 3y = 5. 61) 62) Through (-1, 12), parallel to -3x + 2y = 13 62) 63) Through (-8, 4), perpendicular to 9x - 8y = ) Determine whether the pair of equations represents perpendicular lines. 64) 4x - 6y = -5 36x + 12y = -5 64) 65) 3x - 6y = -4 18x + 9y = -4 65) For the point-slope equation given, state the slope and the point on the graph used in creating the equation. 66) y - 1 = 4(x - 7) 66) 67) y + 4 = 6x 67) 12

13 68) y = 1 (x - 5) 68) 2 69) y = x 69) Graph the line. 70) y - 1 = - 1 (x - 4) 70) 4 71) y - 1 = 1 (x + 3) 71) 2 Find an equation for the described linear function. 72) Through (0, 1) and parallel to y = -9x ) 73) Through 0, 7 8 and perpendicular to 7x - 9y = 3 73) Find an equation in point-slope form of the line having the specified slope and containing the point indicated. 74) m = -4, (-8, 9) 74) 13

14 75) m = 5, (-5, 6) 75) 6 Find an equation of the line having the specified slope and containing the indicated point. Write your answer in slope-intercept form. 76) m = -9; (4, -3) 76) 77) m = 9; (-9, 0) 77) 78) m = 8; (0, -9) 78) Find an equation of the line containing the given pair of points. Write your final answer as a linear function in slope-intercept form. 79) (-4, 7) and (-2, 10) 79) 80) (3, -6) and (7, -6) 80) Solve the problem. 81) The total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. Predict the total sales after 41 months. 81) 82) In 1900 the population of a midwest city was 15,000. By 1910 it had grown to 17,000. If it continues to grow at the same rate, what will the population be in 1932? Give your answer to the nearest whole number. 82) 14

15 Answer Key Testname: CH3TEST 1) A(-5, 0); B(1, -1) 2) Quadrant II 3) None 4) I and IV 5) III and IV 6) I and III 7) II and IV 8) No 9) Yes 10) Yes 11) Show that (7, 5) is a solution: y = x =? =? 5 TRUE Show that (1, -1) is a solution: y = x =? =? -1 TRUE Coordinates of the additional solution may vary but should satisfy y = x ) Show that (6, 1) is a solution: x + 2y = (1) =? =? 8 8 =? 8 TRUE Show that (-4, 6) is a solution: x + 2y = (6) =? =? 8 8 =? 8 TRUE Coordinates of the additional solution may vary but should satisfy x + 2y = 8. 13) 15

16 Answer Key Testname: CH3TEST 14) 15) y = 2 7 x ) y = - x ) (0, -5), (-7, 0) 18) (0, 6), (-3, 0), (-2, 0), (1, 0) 19) (1, 0), (0, 2) 20) (-2, 0), (0, 2) 21) (0, 17) 22) (4, 0) 23) 0, - 1 2, 2, 0 24) (0, 6), (3, 0) 16

17 Answer Key Testname: CH3TEST 25) 26) 27) 28) x = -3 29) y = -1 30) miles per hour, or miles/hour 31) bricks per foot, or bricks/foot 32) $324 per year 33) $0.92/mi 34) 50 miles per hour 17

18 Answer Key Testname: CH3TEST 35) 36) 37) 3 degrees per hour 38) -6 pounds per month 39) ) ) Undefined 42) 0 43) ) Undefined 45) 0 46) ) Undefined 48) 0 18

19 Answer Key Testname: CH3TEST 49) 50) 51) 3 ; (0, -1) 4 52) 15 ; (0, -5) 4 53) 0; (0, 11) 54) y = x ) y = 4x 56) 57) No 58) Yes 59) No 19

20 Answer Key Testname: CH3TEST 60) y = 4 7 x ) y = x ) y = 3 2 x ) y = x ) No 65) Yes 66) m = 4; (7, 1) 67) m = 6; (0, -4) 68) m = 1 ; (5, 0) 2 69) m = - 1 ; (0, 0) 2 70) 71) 72) y = -9x ) y = x ) y - 9 = -4(x + 8) 20

21 Answer Key Testname: CH3TEST 75) y - 6 = 5 (x + 5) 6 76) f(x) = -9x ) f(x) = 9x ) f(x) = 8x ) f(x) = 3 2 x ) f(x) = -6 81) $106,700 82) 21,400 21