Math Checkup Unit 1 Lesson 3 Essays

Math Checkup Unit 1 Lesson 3 Essays Math Checkup Unit 1 Lesson 3 Essay Math Checkup Unit 1 Lesson 3 Essay Essay Topic: A Lesson Before Dying Linear Functions Answer the following questions using what youve learned from this lesson. Write your responses in the space provided, and turn the assignment in to your instructor. 1. What is the slope of the line in the graph below? Show your work. Answer: To find out the slope, you must first take two separate points on the graph, such as (-5,-1) and (0,1). Then, it’s a simple matter to use the equation [pic] to find the slope: [pic]= [pic] 2. What is the slope of the line represented by the table of values below? How do you know? |x |y | |-2 |3 | -1 |4. 5 | |0 |6 | |1 |7. 5 | |2 |9 | Answer: By taking two different (x,y) values from the table and using the [pic] formula, we can easily find the slope. For example, let’s use (-2,3) and (0,6): [pic]= [pic] 3. Which of the following graphs could be the graph of y = 4x 5? Circle the letter of your answer(s) and explain your choice(s). a. b. c. d. 4. Write the equation of the line that passes through the points (3,7) and (-1,2) in: The slope is [pic]=[pic]=[pic] a. Point-slope form -2=[pic](x+1) b. Slope-intercept form y=[pic]x+[pic] 5. What is the slope of a line that is perpendicular to [pic]? Show your work. Answer: A line perpendicular to y=[pic]x would have a slope that’s the reciprocal of the slope to y=[pic]x. So the answer is [pic]. 6. Write the equation of a line passing through (0,6) and parallel to the line [pic]. Answer: y=[pic]x+6 7. Which of the following tables of values could have been generated by a linear function? How do you know? a. |x |y | |-2 | -3 | |-1 |-5 | 0 |-7 | |1 |-9 | |2 |-11 | b. |x |y | |-2 |1 | |-1 |3 | |0 |6 | |1 |10 | |2 |15 | c. |x |y | |-2 |1 | |-1 |1 | |0 |1 | |1 |1 | |2 |1 | Answer:Table A is a linear function, since it has an even distribution in both its x and y values. Table B is NOT a linear function, since it doesn’t have an even distribution in its y values. Table C is a linear function, since it has an even distribution in both its x and y values. 8. For each table in #7 that could have been generated by a linear function, calculate the slope of the line produced by that function. Answer: The rise over run formula [pic] shows the slope of a function table. Table A has a slope of [pic]= [pic]= -2. Table C has a slope of [pic]= [pic]= 0. 9. The cost of hosting a dinner in a particular restaurant is given by y = 18. x + 250, where x is the number of people at the dinner and y is dollars. What is the slope of this function? What does it mean in the context of the problem? Answer: The slope is 18. 5. It means that each person that attends costs $18. 50. 10. The cost of hosting a dinner in a particular restaurant is given by y = 18. 5x + 250, where x is the number of people at the dinner and y is dollars. What is the y-intercept of this function? What does it mean in the context of the problem? Answer: The y-intercept is 250. This means that you must pay $250 BEFORE you pay for each guest’s meal. 11.Write the equation of the line that is parallel to the x-axis and goes through the point (1,4). Answer: y=4 12. Does the point (2,6) lie on the line that connects (1,4) and (0,3)? Explain. Answer: The equation for the slope of (1,4) and (0,3) is y=x+3. Just plug (2,6) into the equation: 6=2+3? No. 6=/=2+3 So, no. (2,6) does not lie in the line that connects (1,4) and (0,3). 13. Which of the following pairs of lines are perpendicular? How do you know? Perpendicular? a. [pic] and [pic]No. Their slopes are NOT negative reciprocals. b. [pic]and [pic]Yes. Their slopes are negative reciprocals. c. [pic]and [pic]No.Their slopes are NOT negative reciprocals. 14. Jeremy uses the linear function G = 12h + 50 to represent the grade, G (in points out of 100), that he can earn on an exam as a function of h, the number of hours he spends studying for the exam. a. Identify the slope and y-intercept of Jeremys function and explain what they mean in the context of the problem. The slope is 12 and the y-intercept is 50. This means that Jeremy’s score, if he didn’t study, would be 50. However, for every hour he studies, his score will go up 12 points. b. If Jeremy spends 3 hours studying for the exam, what grade does he expect to earn?Show your work. G = 12(3) + 50 = 36 + 50 = 86 Jeremy can expect to earn 86 points on the test if he studies for 3 hours. c. How many hours should Jeremy study if he wants to earn a perfect score on the exam? Show your work. 100 = 12h + 50 50 = 12h h = 4 hours, 10 minutes. 15. Suppose that demand, D, for a particular product is given by the function D = 100 2p, where p is the price in dollars of the product and D is the number of products that can be sold at that price. a. What does the slope of this function mean in the context of the problem? The slope shows that for each dollar the price increases, two less items will be sold. b.What price should be set in order to sell 75 items? Show your work. 75 = 100 2p 2p = 25 p = $12. 50 The price should be set as $12. 50 to sell 75 items. 16. Temperature may be given in degrees Celsius or in degrees Fahrenheit. The freezing point of water is 32(F or 0(C. The boiling point of water is 212(F or 100(C. a. Write the equation of a line that shows the relationship between degrees Fahrenheit and degrees Celsius. C=[pic](F-32) b. What is the temperature in Fahrenheit when it is 17oC? 62. 6 Fahrenheit c. What is the temperature in Celsius when it is 79oF? 26. 1 Celsius 17. Write at least three different expressions that mean slope. Answer: Slope=[pic]=[pic]=[pic] 18. In order to write the equation of a line, what two pieces of information do you need? (Hint: there may be more than one answer to this question. ) Answer: You must know both the slope and y-intercept to write the equation of a line. 19. The cost of manufacturing soccer balls is given by C = 24,000 + 7x, where x is the number of soccer balls produced. a. What is the slope of this equation and what does it represent in the context of the problem? The slope is 7, and that means each soccer ball costs $7. b. What is the y-intercept of this equation and what does it represent in the context of the problem?The y-intercept is 24,000, and it means that you have to pay $24,000 BEFORE making any soccer balls. c. If a manufacturer wanted to spend less than $30,000 to produce soccer balls, what is the maximum number of balls that can be produced? Show your work. 30000=24000+7x 6000=7x 857. 14=x The maximum number of soccer balls that can be made without spending above $30000 is 857. 20. Write the equation of a line that is parallel to the line connecting (2,5) and (-1,-4). Answer: y=3x+5 This is the only line with a negative slope and a negative intercept.