Math 60 ELEMENTARY ALGEBRA Xtra Practice: Section 2.7, Chapters 3 and 4
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1 Name of Math lover: my favorite student Date: Math 60 ELEMENTARY ALGEBRA Xtra Practice: Section 2.7, Chapters 3 and 4 Ok to use a calculator (But don t forget to show enough work in order to receive credit) Question: How can I better prepare for Midterm Exam 2? Answer: Review your homework, including the supplemental homework problems that your instructor included with the homework list for Chapter 4. Also, go over your quizzes and lecture notes. 1. What is the x-intercept? What is the y-intercept? Use the x-intercept and y-intercept to graph the line. Label the coordinates of the intercepts. You MUST use a ruler or some other straight edge when graphing your lines. You will be unable to use a note card or a sheet of paper as a straight edge. a. 3x + 6y = 12. b. 8y 2x = 4 Friendly reminder: 1. Sharing of instruments WILL NOT be allowed once the exams have been distributed. (Note: If you are done with the exam, you still cannot share any instruments) 2. At any point during the exam, if you (1) talk to another student, (2) use your cell phone, or (3) use a graphing calculator, then... You will be accused of cheating and will receive a ZERO on the exam NO EXCEPTIONS. Xtra Practice, M60 pg 1 Revised Fall 2017
2 2. Graph each line. a. 2y 8x = 16 b. 5y + 3x = 0 3. Graph the solution set: 9x 3y 12 Xtra Practice, M60 pg 2 Revised Fall 2017
3 4. The equations of two lines are given. Are the lines parallel? Why or why not? 5y 2x = 15 and y = 2x 5. The equations of two lines are given. Are the lines parallel? Why or why not? 3y + 24x = 2 and 3x 24y = 4 6. The equations of two lines are given. Are the lines perpendicular? Why or why not? 5y 2x = 15 and y = 2x 7. The equations of two lines are given. Are the lines perpendicular? Why or why not? 3y + 24x = 2 and 3x 24y = 4 Find the equation of the line satisfying the given conditions. Equations should be written in slope-intercept form. 8. Find the equation of a line that passes through the points (2, 1) and (6, 6). 9. Find the equation of a line with slope 2, passing through the point ( 1, 11). 10. Find the equation of a line with slope 6 5, passing through the point ( 5, 6). 11. Find the equation of a line that passes through the points (6, 13) and (3, 6). 12. Find the equation of a line with slope 0, passing through the point (12, 15). 13. Find the equation of a line with slope undefined, passing through the point (12, 15). Solve the system of equations by graphing x 4y 8 x 2y x 4y 12 20x 80y 0 Xtra Practice, M60 pg 3 Revised Fall 2017
4 16. Find the rate of change represented by each line. Please include the units of measurement. Round your answers to the nearest tenth, if necessary a. b. flow rate (A): flow rate (B): c. d. butter: cream cheese: plant A: plant B: 17. Use the substitution method to solve the system: 3x + 18y = 18 9x 8y = Use the elimination method to solve the system: x + 4y = 4 9x 5y = 5 Solve the system. Please note: Although you can solve the systems by using either the substitution method or the elimination method, if you are going to use the substitution method, to make life easier please make sure that there is at least one good candidate to solve for. If there isn t one, then you will be better off by using the elimination method to solve the system. P.S. It is highly recommended that you check your answer by hand or with the help of a calculator. Why? So that way you don t have to rely on an answer key to see if your answer is correct x 8y = 9 18x + 24y = y = 2x 30 8x + 4y = y = 1 2 x 3 4x 8y = y 6 = 9x 18x + 14y = 12 Xtra Practice, M60 pg 4 Revised Fall 2017
5 Form an equation(s) and solve it to answer the remaining problems. Please write your answer in a complete sentence. Don t forget to use a Let statement, e.g. Let x =, or a where statement, e.g. where x =, to define the variable. Remember: Your variable should be defined either at any time before your equation, or immediately right after you write your equation. 23. Panchito and Conchita leave from opposite ends of a jogging trail 7 miles apart and travel toward each other. Panchito jogs 2 mph faster than Conchita, and they meet after half an hour. How fast does each of them jog? 24. At a movie theater concession stand, three candy bars and two small sodas cost $14. Four candy bars and three small sodas cost $ Find the cost of a candy bar and the cost of a small soda. 25. A group of 27 girl scouts went to Knott s Berry Farm. The amusement park charges $40.00 for adults and $30.00 for children. If the amusement park collected $930 from the group, then how many of them were adults? How many of them were children? 26. Two planes leave the same airport and travel in opposite directions. The northbound plane flies 40 mph slower than the southbound plane. After 1.5 hours they are 1320 miles apart. Find the speed of each plane. Other items to take into consideration: If you haven t been reading your textbook, then what are you waiting for??? You d be surprised what a difference it makes when you go over your notes and also read your textbook. Xtra Practice, M60 pg 5 Revised Fall 2017
6 Formulas to keep in mind for the upcoming midterm exam... What to use... When to use it... y2 y1 Slope formula: m x x 2 1 Use it when you re asked to find the slope of a line. Point slope formula: y y m x x 1 1 Use it when you re asked to find the equation of a line. To find the equation of a line, you need 2 things. (1) a point, and (2) a slope Tip: If you re asked to find the equation of a line, and you re only given 2 points, then don t panic because they didn t give you a slope. Since you have 2 points, then just go ahead and use the slope formula to first find the slope of the line that goes through those two points, and then... Use the point slope formula to find the equation of the line Things to keep in mind for the upcoming exam... Item... Breakdown... Standard Form: Ax By C This is just a way (form) to write an equation. To write an equation in standard form, fix it so you have x-term, y-term = constant, and, don t forget to make sure that your equation doesn t have any fractions or decimals. Slope intercept Form: y = mx + b This is just another way (form) to write an equation. It s called slope-intercept form, because this is a way/form to write an equation where you can easily identify (1) the slope (this is the m), and (2) the y-intercept (this is the b) Good luck to all and happy studying!!! And remember to keep your cool. You got this! I know that you will do great! Xtra Practice, M60 pg 6 Revised Fall 2017
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