Intermediate Algebra Chapter 2.5: The Point-Slope Form of an Equation of a Line Finding equations from graphs: steps: 1. Find the y-intercept.

Transcription

1 Intermediate Algebra Chapter.5: The Point-Slope Form of an Equation of a Line Name Finding equations from graphs: steps:. Find the -intercept. (0, b). Find the slope. rise m run 3. Plug into slope-intercept formula m b. E : Slope: down, right m = - -int: (0, 5), so b=5 Therefore, 5 f ( ) 5 E : Slope: up, right m = ½ -int: (0, ), so b= Therefore, f ( ) 4. Put into function notation b replacing with f(). f ( ) m b You tr: Find the equations of each line. (0, 3) (-7,0) (0,0) (0,-4) (0,6) (-3,0) Finding Equations given a point and a slope: steps:. Plug the point (, ) and the slope, m, that was given into the point-slope formula m( ). E: Write an equation for a line with slope, m, and goes through the point (8, -).. Solve for to get into slope intercept form: m b. 3. Put into function notation b replacing with f(). f ( ) m b

2 You tr: Find the equation of each line.. Write an equation for the line with slope, and it goes through the point (-0, -). 3 m, 5. Write an equation for the line with slope, 3 m, and goes through the point (-8, 0) Write an equation for the line with slope, m 0, and goes through the point (5, -4). 4. Write an equation for the line with slope, m = undefined, and that goes through the point (, 7). Finding Equations given points: steps:. Calculate the slope. m E: Write an equation for a line that goes through the points (4, -3) and (-6, ).. Use the slope, m, and choose either point to plug into the point-slope formula m( ). 3. Solve for to get into slope intercept form: m b. 4. Put into function notation b replacing with f(). f ( ) m b

3 You Tr: Find the equation of each line.. Write an equation for the line that goes through the points (6, -) and (-3, 4).. Write an equation for the line that goes through the points (-7, -3) and (-6, -4). 3. Write an equation for the line that goes through the points (-3, -) and (-3, 4). 4. Write an equation for the line that goes through the points (6, 4) and (-3, 4). Finding Equations that Parallel or Perpendicular to Other Equations: steps: E: Write an equation for the line that goes. Put the equation given in slope intercept form through the point (-6, 4) and perpendicular to to determine the slope, m. the graph of Use the slope, m, to find the parallel or perpendicular slope For parallel lines: -use the same slope, m For perpendicular lines: -use the negative reciprocal of m 3. Plug the point (, ) and the parallel or perpendicular slope, m, that was found in step# into the point-slope formula m( ). 4. Solve for to get into slope intercept form: m b. 5. Put into function notation b replacing with f(). f ( ) m b

4 You Tr: Find the equation of each line.. Write an equation for the line that goes through the point (6, -) and parallel to the graph of 3.. Write an equation for the line that goes through the point (-, ) and perpendicular to the graph of Write an equation for the line that goes through the point (-4, 5) and perpendicular to the graph of Write an equation for the line that goes through the point (3, -7) and parallel to the graph of. 5. Write an equation for the line that goes through the point (, 3) and parallel to the line that goes through the points (, 8) and (4, 0). 6. Write an equation for the line that goes through the point (6, 9) and perpendicular to the line that goes through the points (0, -) and (-5, 8).

5 Finding Equations of Lines in Applications. The graph below shows that the projected value, v, of a Guarneri del Gesù violin is a linear function of the age, a, in ears, of the violin, for 6 a 90. a. Determine the function, v(a) represented b this line. b. Using the function from part a), determine the projected value of a 65-ear-old Guarneri del Gesù violin. c. Using the function from part a), determine the age of a Guarneri del Gesù violin with a projected value of $5million. d. What is the domain and range of this function?

6 . The number of calories burned in hour of biccle riding is a linear function of the speed of the biccle. A person riding at mph will burn about 564 calories in hour and while riding at 8 mph will burn about 846calories in hour. This information is shown below. a. Determine a linear function that can be used to estimate the number of calories, C, burned in hour when a biccle is ridden at r mph, for 6 r 4. b. Use the function determined in part a) to estimate the number of calories burned in hour when a biccle is ridden at 0 mph. c. Use the function determined in part a) to estimate the speed at which a biccle should be ridden to burn 800 calories in hour. d. What is the domain and range of this function?

7 3. The number of calories burned for hour on a treadmill going at a constant speed is a function of the incline of the treadmill. At 4 miles per hour a person on a 5 incline will burn 55 calories. At 4 mph on a 5 incline the person will burn 880 calories. Let C be the calories burned and d be the degrees of incline of the treadmill. a. Use this data to write the calories burned C as a function of the degrees, d, of incline of the treadmill. b. Determine the number of calories burned b the person in hour on a treadmill going 4 miles per hour and at a 9 incline. 4. Lecturer Salar Suppose the annual salar of a lecturer at Chaumont Universit is a linear function of the number of ears of teaching eperience. A lecturer with 9 ears of teaching eperience is paid $4,350. A lecturer with 5 ears of teaching eperience is paid $46,687. a. Use this data to write the annual salar of a lecturer, s, as a function of the number of ears of teaching eperience, n. b. Using the function from part a), determine the annual salar of a lecturer with 0 ears of teaching eperience. c. Using the function from part a), estimate the number of ears of teaching eperience a lecturer must have to obtain an annual salar of $44,908.

8 5. The gas mileage, m, of a specific car is a linear function of the speed, s, at which the car is driven, for 30 s 60. If the car is driven at a rate of 30 mph, the car s gas mileage is 35 miles per gallon. If the car is driven at 60 mph, the car s gas mileage is 0 miles per gallon. a. Use this data to write the gas mileage, m, as a function of speed, s. b. Using the function from part a), determine the gas mileage if the car is driven at a speed of 48 mph. c. Using the function from part a), determine the speed at which the car must be driven to get gas mileage of 40 miles per gallon. 6. The manufacturer of bab strollers determines that the suppl, s, is a linear function of the selling price, p, for $ 00 p $ 300. If a stroller sells for $0.00, then 0 strollers will be supplied per month. If a stroller sells for $30.00, then 30 strollers will be supplied per month. a. Use this data to write an equation for the suppl, s, as a function of price, p. b. Using the function from part a), determine the suppl when the price of a stroller is $0.00. c. Using the function from part a), determine the selling price if the suppl is 35 strollers.