Chapter 3 Graphing Linear Equations

Transcription

1 Chapter 3 Graphing Linear Equations Rectangular Coordinate System Cartesian Coordinate System Origin Quadrants y-axis x-axis Scale Coordinates Ex: Plot each point: (0,0), (-1, 3), (1, 3), (1, -3), (-1, -3)

2 Ex: Give the coordinates of each point: Ex: (#22) Given the following graph that gives the heart rate of a woman before, during and after an aerobic workout. a) What was the woman s heart rate half an hour after beginning the workout? b) For how long did the woman work out at her training zone?

3 3.2 Graphing Linear Equations Ex: List pairs of numbers that satisfy the equation y = x + 1 by constructing a table of values: c) Does (4, 4) satisfy that equation? How about (5, -5)? d) Plot those pairs on a rectangular coordinate system. Do you see a pattern?

4 Ex: Graph 2x y = -3 by solving for y first and then setting up a table of values.

5 3.3 Intercepts Ex: Graph the line y = 3x 6 by finding the x- and y- intercepts and using one more point as a check. Horizontal and Vertical Lines Ex: Graph y = 3 by setting up a table of values.

6 Ex: Graph x = -3 by setting up a table of values. Ex: (Ex 8) Using information about a 2010 Toyota Prius Hybrid, we can set up the equation 12m g = 7200 where m represents the number of miles driven, and g represents the number of gallons of gas left in the tank. Find the intercepts for this line and explain what they represent.

7 3.4 Slope and Rate of Change Ex: Pretend you are going to go skiing down a mountain. Draw examples of the following: a) a very steep slope b) a slightly steep slope c) a flat slope Question: How could we differentiate between going up a mountain and going down a mountain? Question: How could we quantify how steep the slopes are?

8 Slope =!"#$!%& = )*+&,$ "& - )*+&,$ "&. Ex: Graph y = 2x 1 and then, using triangles, calculate the slope between: a) x = 0 and x = 1 b) x = 1 and x = 3 c) x = -1 and x = 1 What do you notice about all three slopes?

9 Using the Slope Formula The slope of the line passing through (x 1, y 1 ) and (x 2, y 2 ) is given by the formula: slope = m = - /0-1. / 0. 1 Ex: Using the slope formula, find these slopes: 1) The slope of the line passing through (-1, 3) and (2, 6) 2) The slope of the line y = 3 3) The slope of the line x = 3

10 Parallel and Perpendicular Lines Parallel Lines: Perpendicular Lines: Ex: Fill in this chart: Slope Parallel Slope Perpendicular Slope 2 =

11 Ex: Determine whether the lines through each pair of points are parallel, perpendicular, or neither. 1) (3, 3) and (4, 4) (3, 3) and (2, 4) 2) (2, 4) and (-1, -1) (8, 0) and (11, 5)

12 3.5 Slope-Intercept Form If you have an equation of a line in this form: 2x y = 5 and you solve for y: then you have Slope-Intercept Form, where Ex: Find the slope and the y-intercept of the line with equation 9x 3y = 10 Ex: Write an equation of the line with slope = -2 and y-intercept (0, 5.4)

13 Ex: Use slope-intercept form to graph 2x + 2y = -6 Ex: Determine whether the graphs of y = 4x + 6 and x + 4y = -2 are parallel, perpendicular or neither.

14 Ex: (#100) A new Playstation 3 costs $ and membership in an online videogame multiplayer network costs $18.49 per month. a) Write a linear equation that gives the cost for someone to buy the machine and belong to the online network for m months. b) Use your answer in part a to find the cost to buy the machine and belong to the network for 3 years.

15 3.6 Point-Slope Form m = Point-Slope Form: y y 1 = m ( x x 1 ) Ex: Find an equation of the line that has slope 5 and passes through(-1, 13). Write the answer in slope-intercept form.

16 Ex: Find an equation of the line that has slope 0 and passes through (3, 4). Ex: Find an equation of the line that passes through (4, 2) and (-1, 12). Write the answer in slope-intercept form.