University:
Glendale Community College
Course:
MAT142 | College Mathematics
Academic year:

2022
Views:

292

Pages:

19
Author:

Bridger Mosley

Chapter 3 practice test #1-2: a) Find the x-intercept b) Find the y-intercept c) Find an additional point d) Sketch a graph 1) 2𝑥 + 4𝑦 = 12 1a) 𝒙 − 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕 (𝟔, 𝟎) 1b) 𝒚 − 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕 (𝟎, 𝟑) 1c) 𝒂𝒅𝒅𝒊𝒕𝒊𝒐𝒏𝒂𝒍 𝒑𝒐𝒊𝒏𝒕 (𝟒, 𝟏) Chapter 3: Lines #1-2: a) Find the x-intercept b) Find the y-intercept c) Find an additional point d) Sketch a graph 1 2) 𝑦 = 𝑥 − 6 2 2a) 𝒙 − 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕 (𝟏𝟐, 𝟎) 2b) 𝒚 − 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕 (𝟎, −𝟔) 2c) 𝒂𝒅𝒅𝒊𝒕𝒊𝒐𝒏𝒂𝒍 𝒑𝒐𝒊𝒏𝒕 (𝟐, −𝟓) #3 – 4 a) Find three points b) Plot the points c) Sketch a graph. d) Use the graph to find the x-intercept (say there is no x-intercept if the graph does not cross the x-axis). e) Use the graph to find the y-intercept (say there is no y-intercept if the graph does not cross the y-axis.) 3) 𝑥 = −5 3a) Any 3 points with 𝒙 = −𝟓 will work. You may have different points. (−𝟓, 𝟎), (−𝟓, 𝟑), (−𝟓, 𝟔) 3b) and 3c) See below 3d) graph crosses x-axis at (5,0) 𝒙 − 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕 (𝟓, 𝟎) 3e) graph does not cross y-axis no y-intercept #3 – 4 a) Find three points b) Plot the points c) Sketch a graph. d) Use the graph to find the x-intercept (say there is no x-intercept if the graph does not cross the x-axis). e) Use the graph to find the y-intercept (say there is no y-intercept if the graph does not cross the y-axis.) 4) 𝑦 + 3 = 8 4a) Any 3 points with 𝒚 = 𝟓 will work. You may have different points. (𝟎, 𝟓), (𝟑, 𝟓), (𝟔, 𝟓) 4b) and 4c) see graph below 5) Sketch the graph of the line. State the value of the slope and of the yintercept, state if there is no y-intercept. 𝑦= −3 2 𝑥+5 𝒚 − 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕 (𝟎, 𝟓) 𝒔𝒍𝒐𝒑𝒆 𝒎 = − 𝟑 𝟐 #6 – 7: Find the slope of the line that passes through the two points. 6) 𝑓𝑖𝑟𝑠𝑡 𝑝𝑜𝑖𝑛𝑡 (1,5) 𝑠𝑒𝑐𝑜𝑛𝑑 𝑝𝑜𝑖𝑛𝑡 (−3,9) 𝒎 = −𝟏 7) 𝑓𝑖𝑟𝑠𝑡 𝑝𝑜𝑖𝑛𝑡 (2,4) 𝑠𝑒𝑐𝑜𝑛𝑑 𝑝𝑜𝑖𝑛𝑡 (2,5) 𝒎 = 𝒖𝒏𝒅𝒆𝒇𝒊𝒏𝒆𝒅 8) 𝑦 = −2 7 𝑥+6 a) Find the slope of the given line equation is written in slope-intercept form. The number in front of the x is the slope. 𝒎=− 𝟐 𝟕 b) Find the slope of all lines parallel to the given line All lines parallel to the given line will have the same slope as the given line. 𝒎=− 𝟐 𝟕 c) Find the slope of all lines perpendicular to the given line. All lines perpendicular to the given line will have a slope that is the negative reciprocal of the slope of the given line. 𝒎= 𝟕 𝟐 9) Use the graph of 𝑓(𝑥) to find the average rate of change from 𝑥 = −1 𝑡𝑜 𝑥 = 1 Average rate of change is −𝟒 10) Use the slope intercept formula to find the slope-intercept form of an equation of a line with 𝑠𝑙𝑜𝑝𝑒 𝑚, passing through the 𝑝𝑜𝑖𝑛𝑡 (𝑥, 𝑦). Write your answer in 𝑠𝑙𝑜𝑝𝑒 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 form. 𝑚 = 2 𝑝𝑜𝑖𝑛𝑡 (5, −4) Answer: 𝒚 = 𝟐𝒙 − 𝟏𝟒 11) Use the point slope formula to find the equation of a line with slope m, passing through the point (x, y). Write your answer in slope-intercept form. 𝑚 = −3 𝑝𝑜𝑖𝑛𝑡 (1,5) Answer: 𝒚 = −𝟑𝒙 + 𝟖 12) Use the point slope formula to find the equation of a line passing through the points(𝑥1 , 𝑦1 ) 𝑎𝑛𝑑 (𝑥2 , 𝑦2 ). Write your answer in slope-intercept form. (6, 8) 𝑎𝑛𝑑 (1, −2) Answer: 𝒚 = 𝟐𝒙 − 𝟒 13) Find the equation of the vertical line passing through the point (x, y). 𝑝𝑜𝑖𝑛𝑡 (2,9) All vertical lines have equations of the form 𝒙=# Just set x = to the x-coordinate of the given point Answer: 𝒙 = 𝟐 14) Find the equation of the horizontal line passing through the point (x ,y). 𝑝𝑜𝑖𝑛𝑡 (1, −3) All horizantal lines have equations of the form Just set y = to the y-coordinate of the given point Answer: 𝑦 = −3 𝑦=# 15) Etta Jane receives a weekly allowance of $8. She gets an additional $1 each day she cleans her bedroom. a) Create an equation of a line that can be used to find the amount of money (M) Etta Jane receives in a week she cleans her bedroom (b) times. 𝑴 = 𝟏𝒃 + 𝟖 𝒐𝒓 𝑴 = 𝑏 + 8 b) What will her allowance be in a week when she cleans her room 2 times? 𝑴 = 𝟐 + 𝟖 = 𝟏𝟎 Her allowance will be $10. #16-17: Solve each system of equations using the substitution method. If the system has no solutions say, that it is inconsistent. If the system is dependent write your answer in the form {(𝑥, 𝑦)|𝑤𝑟𝑖𝑡𝑒 𝑒𝑖𝑡ℎ𝑒𝑟 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛} 16) 𝑦 + 3𝑥 = 9 6𝑥 − 5𝑦 = 31 Answer: (𝟔, 𝟏) #16-17: Solve each system of equations using the substitution method. If the system has no solutions say, that it is inconsistent. If the system is dependent write your answer in the form {(𝑥, 𝑦)|𝑤𝑟𝑖𝑡𝑒 𝑒𝑖𝑡ℎ𝑒𝑟 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛} 17) 𝑥 = −3𝑦 + 12 4𝑥 + 12𝑦 = 48 Answer: dependent: {(𝒙, 𝒚)|𝒙 = −𝟑𝒚 + 𝟏𝟐} 𝒐𝒓 {(𝒙, 𝒚)|𝟒𝒙 + 𝟏𝟐𝒚 = 𝟒𝟖} #18 – 19: Solve each system of equations using the elimination method. If the system has no solutions say, that it is inconsistent. If the system is dependent write your answer in the form {(𝑥, 𝑦)|𝑤𝑟𝑖𝑡𝑒 𝑒𝑖𝑡ℎ𝑒𝑟 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛} 18) 2𝑥 + 3𝑦 = 13 3𝑥 − 6𝑦 = 9 Answer: (𝟓, 𝟏) #18 – 19: Solve each system of equations using the elimination method. If the system has no solutions say, that it is inconsistent. If the system is dependent write your answer in the form {(𝑥, 𝑦)|𝑤𝑟𝑖𝑡𝑒 𝑒𝑖𝑡ℎ𝑒𝑟 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛} 19) 4𝑥 + 2𝑦 = 16 8𝑥 + 4𝑦 = 36 Answer: No solution / inconsistent 20) Etta has quarters and dimes. She has a total of 15 coins and the value of the coins is $3.00. How many of each type of coin does she have? Answer: Etta has 10 quarters and 5 dimes. 21) Kristin wants to make 60 gal. of a 40% alcohol solution by mixing a 20% alcohol solution and a 50% alcohol solution. How much of each solution must she use Concentration 50% 20% 40% (result) Amount Multiply Answer: 40 gallons of 50% solution, 20 gallons of 20% solution.