Unit 5 Study Guide Answers

1. Unit 5 Study Guide Answers

2. 1. Define slope and explain how to find slope from a table of values (chart). • Slope is the measurement of the steepness of a line. • Choose any two ordered pairs. Subtract the y’s and put it in the numerator. Subtract the x’s and put it in the denominator.

3. 2. Find the equation of the line in slope intercept form given the points (5, -9) and (-4, 3). x1 y1 x2 y2 • We need to create an equation of a line that passes through (5, -9) and (-4, 3). • Let’s start with the equation. y = mx + b • We need to replace m and b. • We will find the slope with the slope formula. • We will find the y-intercept by plugging in the slope and one point on the line into the slope intercept form, y = mx + b.

4. 2. Find the equation of the line in slope intercept form given the points (5, -9) and (-4, 3). x1 y1 x2 y2 Slope = m = rise = y2 – y1 formula run x2 – x1 m = 3- (-9)Keep change change +3 + + 9 -4 – 5 -4 + -5 m = 12 = 4 or -4It doesn’t matter where -9 -3 3 the negative is.

5. 2. Find the equation of the line in slope intercept form given the points (5, -9) and (-4, 3). x1 y1 x2 y2 y = mx + b Substitute the slope and a point on the line. -9 = -4 (5) + b 3 -9 = -20 + b Change the -9 to a fraction -27/3 (same denominator) 3 -27/3 = -20/3 + b 20/3 20/3 -7/3 = b y = -4/3 x -7/3 answer (Sorry, didn’t realize that the problem was so stinky.)

6. 3. A clothes designer manufactures 121 pairs of jeans every 11 minutes. What is the slope of the line? What does it represent? • 121(rise) / 11 (run) = 11 • 11 pair of jeans are made every minute

7. 4. What is the slope of the graph of the linear function given by this pattern: 6, 3, 0, -3, -6, …?a) -6 b) -3 c) 3 d) 6 • Remember that slope is change. The change in this sequence is also called the common difference. The difference between each number is -3. Answer = b

8. 5. If you graph the line x = 14, what type of slope would it have?a) positive b) negative c) zero d) undefined • Do you remember from the unit about functions. I told you that if you see x = number, the line is vertical. • What kind of slope does a vertical line have? • Do the arm test? Answer = D) undefined

9. 6. What is a y-intercept? In slope-intercept form, what is the variable that represents it? The y-intercept is where the line crosses the y-axis. The variable is b.

10. 7. Daniel has $50 saved and makes $5.00 per hour working. Determine the equation of the line to determine how much money Daniel would have working any number of hours. From this information, identify the y-intercept. (Starting Point) a) .10 b) 50 c) 10 d) 5 • We would set up the problem like this, y = 50 + 5x. • Since we are talking about slope intercept formula, I am going to switch the 5x and 50 and get, y = 5x + 50. • Remember, the y-intercept is the starting point for the graph. • In this equation, we are starting at $50, which is also the y-intercept. Answer = b.

11. 8. Determine the equation of the line from the graph. • What is the y-intercept? • 2 • What is the slope? (Count rise/run) • 1/2 • Now you can create the equation in slope intercept form. • y = ½ x + 2

12. 9. An amusement park will provide lunch for one person for $4, two people for $6, three people for $8, etc… Write an equation that models the price of lunch as a function of the number of people eating. We are deleting #9 because we have not gone over it. In its place, you will be determining if a graph has a positive, negative, zero, or undefined slope. Let’s get those arms moving.

13. We are going to put the equation of the line in slope-intercept form, y = mx + b. We need to replace m & b. • Can we figure out m or b from the table? • (0, 2) is the point on the line where it crosses the y axis, the y intercept. So 2 is b. • We get m by taking two points, any two points, and plugging them into the slope formula. m = rise = y2 – y1 run x2 – x1

14. m = rise = y2 – y1 = 6 – 2 = 4 = 4 run x2 – x1 1 – 0 1 5. Now we can plug m & b into y = mx + b. Answer is y = 4x + 2

15. 11. A limo company charges a base rate of $45 and $3 per mile. Which equation show the total cost of a ride in the limo?a) y = 3x+ 45 b)y = 45x+23 c) y = 3x + 45y d) y = 3x - 45 • We learned about this in another lesson. Since $45 is a one-time charge, it will not have a variable next to it. Remember Costco, the membership fee and the T-shirts? • We would write the equation as y = 45 + 3x. • Here is the problem, you might say that you cannot find the answer. It’s here. We are just flip flopping the 45 and the 3x. Answer is y = 3x + 45

16. We talked about this in a previous lesson. • When a line is horizontal, the equation is y = ? Answer is a) y = 2

17. -3x – y = 2 • 2x – 3y = 9 • 3x + y = 9 • x + y = 3 • The easiest way for you to solve is for you to plug BOTH points into each equation. If the left and right side of the equals is the same, you have the right equation. • This means that you take a point, plug the x coordinate into x and the y coordinate into the y of the equation. Answer is c) 3x + y = 9

18. 14. How do you know whether to shade above or below the line when graphing an inequality on the coordinate plane? • You shade above the line when the inequality sign is > or ≥. You shade below the line when the inequality sign is < or ≤.

19. 15. Stephen makes $8 per hour working at QT and $4 per hour babysitting. He wants to save at least $60 to spend at the game store. Write an inequality that represents the hours he needs to work to reach his goal. Graph the inequality and give an example of possible hours to work. • Q = # of hours worked at QT • B = # of hours worked babysitting • The equation is 8Q + 4B ≥ 60 He could work 8 hours at QT and 0 hours babysitting.

20. 15. Stephen makes $8 per hour working at QT and $4 per hour babysitting. He wants to save at least $60 to spend at the games store. Write an inequality that represents the hours he needs to work to reach his goal. Graph the inequality and give an example of possible hours to work.

21. 16. Graph the inequality y > 3x - 1 • Graph the line y = 3x – 1 • Look at the inequality to see what kind of line to draw. • Look at the inequality to see where to shade.

22. 17. What is the graph of the solution set of y ≤ -2x – 2? • the open half plane above the graph of y = -2x – 2 • the closed half plane above the graph of y = -2x – 2 • the open half plane below the graph of y = -2x – 2 • the closed half plane below the graph of y = -2x – 2 • Look at the inequality. • The “or equals” sign means that that it is a closed half plane. • The inequality is less than so it will be below the line. • Answer is d).

23. 18. Explain how you estimate the line of best fit from a scatter plot. • You look for a correlation (positive, negative, none) and then draw a line that separates the coordinates where there is close to an equal amount of coordinates above and below the line to estimate the line of best fit.

24. 19. Janie wants to make a scatter plot comparing the life expectancy (vertical axis) and the number of cigarettes smoked (horizontal axis). What type of line of best fit should Janie expect her scatter plot to show? The answer is c).

25. x = 50 • y = 0.25x + 25 • y = x + 40 • y = -6 + 100 • 5 • Draw the line of best fit. • Come up with an equation in slope intercept form, y = mx + b • Can you determine m or b from the graph. Yes, both. • 40 is the y-intercept because that is where the line crosses the y axis. • Determine the slope, rise over run. • Now, plug in m & b into the slope intercept form. • The answer is c.