Algebra 1 Name: ___________________________________ Sections 4.1-4.3 Writing linear equations in slope-intercept and point-slope form Quiz review 1. Write an equation in slope-intercept form for the line shown. a. b. 2. Write an equation in slope-intercept form of the line that passes through the points a. (0, 8) and (6, 3) b. (3, 4) and (3, 3) 3. Write an equation in slope-intercept form of the linear function f with the values a. f (5) 4 and f (4) 2 b. f (2) 3 and f (5) 5 4. Write an equation that represents the linear function shown in the table or mapping diagram. a. b. x f(x) –8 –2 –4 –1 4 1 For each of the following, (a) write an equation in point-slope form of the line that passes through the given point and has the given slope and (b) rewrite the equation in slope-intercept form. 5. (4, 5); m 6 6. (8, 2); m 3 4 For each of the following, (a) write an equation in point-slope form of the line that passes through the two points and (b) rewrite the equation in slope-intercept form. 7. (4, 7) and (5, 1) 8. (3, 8) and (7, 2) For Problems 9-12, graph the equation by (1) identifying the slope and the point that was used to write the equation, (2) plotting the point and using the slope to find a second point, and (3) using the two points to draw the line. 9.. 13. 10. 12. 11. 14. 15. For Part (a) of Problems 16-18, (1) state the variables, including units; (2) determine the given information (slope, y-intercept, one point, two points?), including units; (3) if needed, find the missing slope and/or y-intercept, including units; and (4) write the equation in slope-intercept form. 16. Rufus has collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. a. Write a linear equation in slope-intercept form to model the situation. b. In how many weeks will Rufus have a total of 400 pounds of cans? 17. A canoe rental service charges a transportation fee and $8 dollars an hour to rent a canoe. Mary and Joe rented a canoe for 6 hours, and the total cost for was $68. a. Write a linear equation in point-slope form to model the situation. b. Rewrite the equation in slope-intercept form. c. What is the transportation fee? d. What is the cost of renting the canoe for 4 hours? 18. An attorney charges a fixed fee for an initial meeting and an hourly fee for all hours worked after this meeting. The attorney charges $850 for an initial meeting and 4 hours of additional work. S/he charges $1750 for an initial meeting and 10 hours of additional work. a. Write a linear equation in point-slope form to model the situation. b. Rewrite the equation in slope-intercept form. c. What is the fee for the initial meeting? What is the hourly fee? d. If the attorney charges a client $2350, how long did the attorney work after the initial meeting? Answers: 1. a. y 5 x 5 , b. y 3 x 8 ; 5 7 1 2. a. y x 8 , b. y x 6 6 2 2 5 3. a. f ( x) 2 x 6 , b. f ( x) x 3 3 1 4. a. y x 6 , b. y x 4 5. a. y 5 6( x 4) , b. y 6 x 29 3 3 6. a. y 2 ( x 8) , b. y x 4 4 4 7. a. y 7 6( x 4) or y 1 6( x 5) , b. y 6 x 31 3 3 3 25 8. a. y 8 ( x 3) or y 2 ( x 7) , b. y x 2 2 2 2 9. m 3, (2, 4) ; 10. m 2, (2, 3) ; 11. m 3, ( 6, 1) ; 5 12. m , (3, 4) 2 1 1 13. y 3 ( x 4) , 14. y 1 3( x 3) , 15. y 1 ( x 1) 4 2 16. a. x = number of weeks; y = pounds of aluminum cans; m = 25 lbs/wk; b = 100 lbs y 25 x 100 b. Rufus will have 400 pounds of cans in 12 weeks. 17. a. x = number of hours; y = total cost, $; m = 8 $/hr; x1 , y1 = (6 hrs, $68) y 68 8( x 6) b. y 8 x 20 c. The transportation fee is $20. d. The cost of renting the canoe for 4 hours is $52. 18. a. x = number of hours; y = total cost, $; x1 , y1 = (4 hrs, $850); x2 , y2 = (10 hrs, $1750); m = 150 $/hr; y 850 150( x 4) or y 1750 150( x 10) b. y 150 x 250 c. The fee for the initial meeting is $250. The hourly fee is $150. d. The attorney worked14 hours in addition to the initial meeting if the charge was $2350.