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|Interpret equation an equation written y = mx + b |You Try |

|Slope: change of y’s over x’s |1. The water filling up in a bathtub is modeled by the equation V=.4t + 3 |

|Y-intercept:value of x when y is 0 (or starting time) |where V is the volume (gallons) and t is the time (minutes) after 8:00 P.M.|

| |What is the meaning of the y-intercept in the problem? |

|Ex: The cost of a rental car is y = 0.50x + 40 where x is the number of |A. The average rate that the bathtub is filling up |

|miles. |B. The amount of water in the tub once it is filled |

|Slope: 0.50 is cost per mile |C. The amount of water at 8:00 PM |

|Y-intercept: $40 is the cost of the car with zero miles |D. The amount of gallons the bathtub is increasing by each minute. |

| | |

|Setting up linear equations: y = CHANGE*x + STARTING |2. What is the meaning of the slope in previous problem? |

|y = mx + b |A. The average rate that the bathtub is filling up |

|(If the x-unit isn’t 1 then divide by the number to find the cost for 1 |B. The amount of water in the tub once it is filled |

|unit. Ex: $2 per ¼ mile become 2/(1/4) or $8 per mile) |C. The amount of water at 8:00 PM |

|Ex: Fancy Flower Company charges 1.5 dollars per ½ mile plus 5 dollars. |D. The amount of gallons the bathtub is increasing by each minute. |

|Write an equation that models the situation: | |

|1.5/( ½) = 3 so C = 3m + 5 |3. The rainfall during an evening storm is given by the following equation:|

| |R= 0.3t + .5 where R is the amount of rainfall (inches) and t is the time |

|Solving linear equations: |(hour) since 9:00 PM. What is the slope and what does it represent? |

|Solve algebraically by looking for x or y |A. 0.3; the amount of rain falling each hour after 9:00 PM |

|OR 2) Type equation into y= and look at the table. |B. 0.5 ; the amount of snow at midnight |

| |C. 0.3; the time it takes to increase by 1 inch |

|Example: Using the previous, example, how far did the flower company |D. 0.5; the amount of rain each hour |

|deliver if the bill was $20? | |

|1) 26 = 3m + 5 |4. A taxi complany charges $2.80 plus $.60 per .3 miles traveled. How much|

|21 = 3m (subtract 5) so m = 7 miles |did the taxi charge for a 10 mile trip? |

|OR 2) Type y = 3x + 5 into Y= |A. $8.80 B. $4.60 C. $22.80 D. $30.60 |

|Look at table for when y = 20 |A tax |

| |5. Sandy is saving money to buy a $140 dress. She has |

|If given two situations to choose from then type situation 1 into y1= and |saved $40 and her parents give her $10 a week. Which |

|situation 2 into y2= and look at the table. |equation can she use to figure out how many weeks, w, it |

|Ex: B balloons charges $2 per mile plus $6 and C Balloons charges 3$ per |will take her to save enough money to buy a dress |

|mile. After how many miles will the companies have the same charge? |assuming that she doesn’t spend any of the money she |

|Y1 = 2x + 6 (B) Y2= 3x (C) |earns? |

|Look at table for same Y value Ans: 6 miles |A. 140 = 40w + 10 B. 140= 10w + 40 |

|Linear Regression TIME IS ALWAYS X. |C. 140 = (7w) + 40 D. 140 = 40(w/7)+ 10 |

|YEARS (Find other years from subtracting from the first year. Example: | |

|1950, 1956, 1965 ( 0, 6, 15 |6. Flavo Yogurt store charges $0.20 per ounce of frozen |

|Chart/Table ask for predictions or equation |yogurt. Chili Yogurt store charges $1.20 plus $.05 per |

|CALCULATOR: [STAT]->EDIT->X values in [pic] Y values in [pic] |ounce of frozen yogurt. How many ounces of yogurt will |

|([STAT] ( CALC 4:LINREG(ax+b) ( [VARS] ( Y-VARS |yield the same price for both stores? |

|(FUNCTION ( 1:[pic] |A. 6 ounces B. 8 ounces C. 10 ounces D. 12 ounces |

|Predict values, label x and y values | |

|Predict Y Value: |7. Pizzaroof charges $9.50 for a large pizza plus a certain |

|Searching the TABLE: |amount per topping. Kevin ordered a two topping pizza |

|[2ND], [WINDOW], TblStart = # |and was charged $11.20. Lucy ordered a large pizza and |

|[2ND], [GRAPH] (table) |was charged $12.90. How many toppings did she order? |

|OR |A. 3 B. 4 C. 5 D. 6 |

|Finding a specific VALUE: | |

|[2ND] – [TRACE] (calc) – 1:Value – [ENTER] - # - [ENTER] | |

| |8-11. Consider the following table of information comparing how much |

|Predict X Value: |students studied and their grade on a test. |

|[pic] equation of line |Hours Studied |

|[pic] y value given |Grade by % on Test |

|[2nd] [CALC]->5:INTERSECT | |

|scroll cursor to intersection, [ENTER] [ENTER] [ENTER] |3 |

|Ordered pair will represent intersection, use x value |80 |

| | |

| |2 |

| |71 |

|Miles driven | |

|25 |4 |

|75 |90 |

|150 | |

|200 |5.5 |

|225 |98 |

| | |

|Gallons in tank |3 |

|15 |83 |

|13 | |

|10 |1 |

|8 |65 |

|? | |

| |0 |

|Do linear regression with all but 225 |60 |

|Equation: y = 16 - .04x | |

|Now plug in 225 for x and get 7 | |

|Slope: The number of gallons decreases by .04 per mile | |

|Y-intercept: 16 gallons in the tank with 0 miles driven | |

| | |

|Interpreting Lines Same process as above. | |

|Given 2 situations and ask to predict | |

|Ex: In 1990 milk cost $1.30 [situation 1] and in 2010 milk cost $3.78 | |

|[situation 2]. Predict the cost of milk in 2024. | |

|CALCULATOR: [STAT]->EDIT->X values in [pic] Y values in | |

|[pic]->[STAT]->CALC: 4:LINREG(ax+b) -> [VARS]->Y-VARS->FUNCTION: 1:[pic] |8. Find the line of best fit that describes the relationship of hours |

|Use information to total |studied to test grades. |

| | |

| |9. Predict what a student who studied 5 hours was expected to score on the|

| |test. |

| | |

| |10. What does the y-intercept represent? |

| | |

| |11. What does the slope represent? |

| | |

| |12-14. Consider the following table of information that represents the cost|

| |of a home in Olde Georgetown neighborhood. |

| |Years |

| |Cost in Thousands |

| | |

| |1950 |

| |96 |

| | |

| |1960 |

| |148.4 |

| | |

| |1970 |

| |212 |

| | |

| |1980 |

| |247.2 |

| | |

| |1990 |

| |274.6 |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

| |12. Write the equation for the line of best fit for the data that |

| |represents the cost in years since 1950. |

| | |

| |13. What is the best estimate for the cost in 2020? |

| | |

| |14. Approximately what year will the cost be $450,000? |

| | |

| |15. The cost of gas in 1998 was $1.03. The cost of gas in 2005 was $2.97. |

| |Assuming the increase is linear, what would be the approximate cost of gas |

| |in 2013? |

| | |

| |16. Sarah opened an account with $300. She is saving for a new car. She |

| |needs to save a total of $4500. She earns $120 a week of which she saves |

| |$100. Write an equation that can be used to determine how many weeks it |

| |will take for Sarah to save enough money. |

| | |

| |17. In 1903 a soda was $0.03. In 2011 a soda is $1.25. Find the average |

| |yearly increase. |

| | |

| |18. The price of a movie ticket in 2002 was $3.50, the price in 2009 was |

| |$5.50. What does the y-intercept represent? |

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