Parallel and Perpendicular Lines Write the equation of a line that passes through a given point, parallel to a given line. Write the equation of a line.

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Presentation transcript:

Parallel and Perpendicular Lines Write the equation of a line that passes through a given point, parallel to a given line. Write the equation of a line that passes through a given point, perpendicular to a given line.

Parallel lines Lines in the same plane that do not intersect are called parallel lines. Parallel lines have the same slope.

Perpendicular Lines Lines that intersect at right angles are called perpendicular lines. The slopes of these lines are opposite reciprocals. Opposite reciprocals???? 3…..

From the given equations, determine if the corresponding lines are parallel, perpendicular, or neither. y = 2x + 2 y = 4x - 2 2x + 6y = 1 4x + 12y =3 neither perpendicular parallel

Write the slope intercept form of an equation for the line that passes through (12,3), and is parallel to the graph of y = 4x – 5 Using the same slope we have m = 4 and (12,3) Point-slope form y – 3 = 4 ( x – 12 ) y – 3 = 4x – 48 y = 4x – y = 4x - 45

Write the slope intercept form of an equation for the line that passes through (3,5), and is perpendicular to the graph of y = ½ x – 5 Using the negative reciprocal of the slope we have, m = -2 Point-slope form y – 5 = -2 ( x – 3 ) y – 5 = -2x + 6 y = -2x y = -2x + 11

Write an equation that is parallel to y= 3x – 8 and passes through the point ( 2, 5 )

Write an equation that is parallel to y= -2x – 8 and passes through the point ( 1, -2 )

Write an equation that is parallel to y= 7x + 1 and passes through the point ( -4, -2 )

Write an equation that is perpendicular to y= -8x + 1 and passes through the point ( 1, 6 )

Write an equation that is perpendicular to y= 2/3x + 6 and passes through the point ( 1, 7 )

Bell Work 1. Find the equation of a line that passes through the point (1, 6) and perpendicular to y = - ½ x – 5.

2. Find the equation of a line that passes through the point (-2, 4) and perpendicular to y = - ¼ x – 5.

3. Find the equation of a line that passes through the point (-3, 1) and perpendicular to y = - 1/8 x – 5.

4. Find the equation of a line that passes through the point ( 6,-2) and perpendicular to y = 2/3 x – 11.

5. Find the equation of a line that passes through the point ( 2, 9) and perpendicular to y = -3/4 x + 2.

Word Problems Involving Linear Equation in Two Variables.

Sample Problems. 1. A taxi company charges a flat fee of P30.00 for riding a taxi and an additional P per kilometer. i. Write an equation to find the cost of a taxi ride. Let x represent the number of kilometers and y represent the total cost. ii.How much is the cost of an 8-km taxi ride?

Solution Representation: x – number of kilometers y – total cost Equation: y = 25x + 30 Solution: (cost of an 8 km taxi ride) y = 25x + 30 y = 25(8) + 30 y = y = P Final Answer

2. The cost to take a taxi from the airport is a linear equation of the distance driven. The cost for 3, 6, and 12 km are shown in the table. A. Write an equation in slope-intercept form that represents the Equation. B. How much is the cost of a 60 km ride? Distance (km)Cost (P)

Solution: Representation: x – number of kilometers y – total cost Equation: y = 3x + 5 Solution: (Cost for a 60 km trip) y = 3x + 5 y = 3(60) + 5 y = y = P Final Answer

Try this! A recording studio charges musicians an initial fee of P5,000 to record an album. Studio time costs an additional P3,500 per hour. a.Write an equation that gives the total cost of an album as a function of studio time (in hours) b.Find the total cost of recording an album that takes 10 hours of studio time.

Board Drill The initial fee to have a website set up using a server is P480. It costs P440 per month to maintain a website. What is the total cost of setting up and maintaining the website for 6 months?

Board Drill The cost of renting a car is P500 a day plus P20 per km travelled. Find the cost of renting a car that will be used for a 150 km trip.

Board Drill A taxi company charges a flat fee of P45 for riding a taxi and an additional P 30 per kilometer. How much is the cost of an 20-mile taxi ride?

The cost to take a taxi from the airport is a linear equation of the distance driven. The cost for 4, 8, and 16 km are shown in the table. How much is the cost of a 80 km ride? Distance (km)Cost (P)

Board Drill A