Linear Equations Revisited Four Important Formulas: Math 8. Slope: Slope-Intercept Form: y mx b. Standard:
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1 Linear Equations Revisited Four Important Formulas: Slope: m x x Slope-Intercept Form: mx b Standard: Ax B C Point-Slope: m x ) ( x You should be able to convert equations easil. Example: Convert to slope-intercept form.. x 5 0 Practice: Convert to slope-intercept form.. 7 x. x 5. 5x 4 Example: Convert to Standard form.. x 4 Practice: Convert to Standard form.. x. 4 x..x 4. 5
2 Slope-Intercept and Standard Form Convert Each into Slope-Intercept Form. 9 x. 5x 0 Name Period. 9 8 x 4. x 7 5. x 9 6. x x 0 8. x 4 9. x 0. 4 x 6
3 Slope-Intercept and Standard Form Convert Each into Standard Form. List -A/B and C values.. x 5. 5 x 7 Name Period Equation: -A/B: Equation: -A/B:. 4. x x 5 Equation: -A/B: Equation: -A/B: 5. x 4 x 6. Equation: -A/B: Equation: -A/B: x x 4 Equation: -A/B: Equation: -A/B:
4 Linear Equations Revisited If ou can convert equations easil, ou can answer questions about the points, slopes, and intercepts of linear equations. Practice: Solve.. What is the slope of the equation 5x 4 0?. What is the -intercept of the equation x 6?. Which of the following equations has a slope of / and a -intercept of 4? A. x B. x C. x Graphs: You should also be able to recognize graphs and write equations for them. Practice: Solve.. Find the slope of each.. Write a slope-intercept form equation for each.. Convert each equation into Standard Form. 4. What is the x-intercept of each line?
5 Intercepts Revisited Intercepts: The x-intercept alwas occurs where equals. The -intercepts alwas occurs where x equals. Set =0 to find the x-intercept. Set x=0 to find the -intercept. Examples: Find the x and -intercepts of each. This is the coverup method.. x. x 5 4. x 8 Practice: Find the x and -intercepts of each. x. x 7. x Practice: Graph each of the following using the intercepts:. 5x 5. x 8. x 9
6 Standard Form and Intercepts Determine the x and -intercepts for each equation below. Convert to Standard Form where necessar. Name Period. 9 x. 5x x 4. x 7 5. x 9 6. x 5 7. x 8. x 4 9. x 0. 4 x 5 x. 5 9 x. 9
7 Standard Form Graph each equation below using the intercepts. Connect the intercepts. Intercepts are all whole numbers.. 6 Name Period x 4. 6x 5. 6 x 6. x 0
8 Points and Equations Points are all ou need to determine the equation of a line. This can be done man was. Example: Match each point below with the equation of the line that passes through it. (. (, ). (,) 4. (,)., ) A. 5 x B. x 5 9 C. x 4 D. x 5 9 If ou are given two points, ou can write an equation of a line. Example: Find the equation in slope-intercept form of the line which passes through the following points: (, 7) and ( 4, 0). Find the slope.. Plug the slope into slope-intercept form and solve for the intercept (b). Practice: Write an equation in slope-intercept form for each:. A line with a slope of - which passes through the point (, ). A. x B. x C. x. A line with a slope of which passes through the point 6, 7) (.. A line which passes through 4, ) ( and ( 6, 8).
9 Points and Equations Practice: Find the slope given each pair of points.. (,5)(4,6). (, )(5, ) Name Period _. 4, )(9,4 ) ( 4. (,0)( 5, ) 5. ( 6,)(, ) 6. (,5)(, 6) Practice. Write the slope-intercept form equation for each: 7. A line with a slope of - that passes through (-4, 5) A line which has a slope of / and passes through (6, -) A line that passes through (-6, -6) and (9, -). 9.
10 Points and Equations Name Period Practice: Each point on the right belongs with one of the equations on the left. Match each point with its proper equation. 0. x 7. x 6 A. (0,4) B. (,). x 5 C. (, ). x D. (5,4) 4. 5x 5 E. ( 7, 0) 5. x 6 F. ( 4, ) 6. x 5 8 G. ( 4, 9) 7. x 7 H. (4,5)
11 Word Problems and Equations Most linear equations are eas to translate into Algebra: Example: Tina mows lawns around her neighborhood. She charges a flat fee of $5, plus she charges $0 per hour for the time it takes for her to mow the lawn. A. What equation could be used to represent the cost (c) of mowing based on the number of hours (h) it takes for her to mow the lawn? B. If it takes an hour and a half to mow a lawn, how much does Tina charge? C. Tina agrees to waive the flat fee for mowing our lawn (because ou live next door), but she charges $4 per hour because our lawn is on a steep slope. If it takes Tina 45 minutes to mow our lawn, how much will it cost? D. In part C, how much do ou save compared to Tina s standard charges? Practice: Write a slope-intercept form equation for each.. The cost of a phone call is $0.75 to connect and $0.07 per minute.. A babsitter charges $0 initiall and $5 per hour.. Equipment at Putt-Putt costs $4 to rent, and is costs $5 per hour to pla. Practice: Harr s lawn service collects leaves each fall for a fee. The charge is $5 to come to our house, and $.50 per bag of leaves the remove. A. What equation could be used to represent the cost (c) to remove leaves based on the number of bags (b) that are collected? B. What is the cost to remove 0 bags of leaves? C. If ou paid $6 for leaf removal, how man bags of leaves were removed from our lawn? D. In the spring, Harr reduces the initial fee to $5, but charges $ per bag. If ou want bags of leaves removed, is it cheaper in the spring or the fall?
12 Word Problems Write an equation to represent each situation given below in the form listed. Convert each to the form listed.. Tomm s Pizza Den charges $7 for a medium pizza plus $0.75 per additional topping. Slope-Intercept Form: (use c for charge and t for toppings) Name Period Standard Form:. A taxi ride in Boston costs $5.50 plus $0.40 for each /5 of a mile. Slope-I ntercept: (c for cost and m for miles... remember to find the cost per mile) Standard:. A long distance compan charges a $0.80 connection fee, plus $0. a minute. Slope-Intercept Form: (use m for minutes and c for charge) Standard Form: 4. When pricing drinks at the convenience store, the manager charges $0.04 per ounce and $0.40 for the cup. Slope-Intercept: (Use n for ounces and c for cost) What would be the price for a -ounce cup of soda?
13 Word Problems Name Period Write an equation to represent each situation given below in the form listed. Answer the question that follows. 5. The cost to produce a book depends on how man copies are printed. For copies, the printing cost of each book is $0.04 per page plus $5.00 for cover/binding. Slope-Intercept Form: What would be the cost to print 500 books if each is 0 pages? 6. To re-shingle the roof of a house, the initial fee is $50 and there is a charge of $.0 per square foot of roof. Slope-Intercept: (c for cost and f for ft ) If it costs $,00 to have our roof re-shingled, how man square feet of roof do ou have? (Just plug-in $00 for c in the equation above and solve for f). 7. A rental car compan charges $4.50 per da of rental plus $0.50 per mile. Write an equation below which uses d for das and m for miles to give ou the cost (c) to rent a car from the compan. A. If ou rented the car for 4 das and drove 80 miles, what would ou pa for the rental? B. If ou rented the car for 7 das and were charged $06.50, how man miles did ou drive the rental car?
14 Review: Linear Equations Practice: State the slope of each using the given information. 00. x x (, ) and ( 5, ) 400. (, 5) and (,4) 500. x-intercept: -intercept: 7 Intercepts: State the x and -intercepts of each: x 00. 5x x ( x ) 5x x 5 4 Practice: Bob s Pools maintains pools during the summer months. The come out once a week to clean and maintain our pool. The charge $8.95 each week plus an additional amount based on the pool s size equal to $0 per 5,000 gallons. 00. What is the weekl cost to maintain a 5,000 gallon pool? 00. Write an equation for the cost (c) based on the number of gallons (g). Remember to find the cost per gallon first! 00. David pas $55.95 per week to have his pool maintained. How man gallons of water are in his pool? 400. Bob waives the $8.95 fee for communit pools larger than 50,000 gallons. How much more will it cost to service a 48,000 gallon pool than it will cost to service a 5,000 gallon pool?
15 Name Period Practice Quiz: Linear Equations Rev. State the slope of each using the given information:., ) ( ( 9, 5). m= 4 5. x 7. m=. x x 4. m= 4. m= State the -intercept of each equation below: 5. 4x 5. -int. 6. x 7. x 5 8. x 6. -int. 7. -int. 8. -int.
16 Name Period Practice Quiz: Linear Equations Rev. Write an equation in slope-intercept form using the information given 9. Slope: Passing through: ( 6, ) 9. = 0. Passing through: (,) and ( 5, ) 0. =. Slope: Passing through: ( 6, ). = Solve each: 5. Convert to standard form (Ax+B=C): x 4.. Megan babsits the Talor twins for $5.50 an hour and usualll gets a $5 tip. Write an equation for the amount Megan charges (c) for babsitting the twins based on the number of hours (h) she works Tom s tow compan charges $5 to come get our car and $.5 per mile to transport it. 4. How much will it cost to have Tom come get ou and tow our car 4 miles? You have $40. How far can ou have Tom tow our car? What equation could be used to represent the cost of towing our car if Tom increases his rate per mile b 5 cents? Most salespeople earn mone based on commission. Earl is a salesman who earns $0,000 per ear plus an amount equal to 6% of his total sales. Write an equation for Earl s earl earnings (e) based on his total sales (t)? 7.
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