8 1 Graphing Linear Equations Warm Up Problem

8 -1 Graphing Linear Equations Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

8 -1 Graphing Linear Equations Warm Up Solve each equation for y. 1. 6 y – 12 x = 24 y = 2 x + 4 2. – 2 y – 4 x = 20 y = – 2 x – 10 3. 2 y – 5 x = 16 y = 5 x + 8 2 4. 3 y + 6 x = 18 y = – 2 x + 6

8 -1 Graphing Linear Equations Problem of the Day The same photo book of Niagara Falls costs $5. 95 in the United States and $8. 25 in Canada. If the exchange rate is $1. 49 in Canadian dollars for each U. S. dollar, in which country is the book a better deal? Canada

8 -1 Graphing Linear Equations Sunshine State Standards MA. 8. A. 1. 6 Compare the graphs of linear and non-linear functions for real-world situations. Also MA. 8. A. 1. 1, MA. 8. A. 1. 5

8 -1 Graphing Linear Equations Vocabulary linear equation rate of change

8 -1 Graphing Linear Equations A linear equation is an equation whose solutions fall on a line on the coordinate plane. All solutions of a particular linear equation fall on the line, and all the points on the line are solutions of the equation.

8 -1 Graphing Linear Equations If an equation is linear, a constant change in the x-value corresponds to a constant change in the y-value. The graph shows an example where each time the x-value increases by 3, the y-value increases by 2.

8 -1 Graphing Linear Equations Additional Example 1 A: Graphing Equations Graph the equation and tell whether it is linear. y = 3 x – 1 +1 x y – 1 – 4 +1 0 – 1 +3 +3 +1 1 2 2 5 +3 Make a table of ordered pairs. Find the differences between consecutive data points.

8 -1 Graphing Linear Equations Additional Example 1 A Continued The equation y = 3 x – 1 is a linear equation because it is the graph of a straight line and each time x increases by 1 unit, y increases by 3 units.

8 -1 Graphing Linear Equations Caution! Be careful when graphing each ordered pair. Double check each point you plot.

8 -1 Graphing Linear Equations Additional Example 1 B: Graphing Equations Graph the equation and tell whether it is linear. y=2 The equation y = 2 is a linear equation because it is the graph of the horizontal line where every y-coordinate is 2.

8 -1 Graphing Linear Equations Check It Out: Example 1 A Graph each equation and tell whether it is linear. y = 2 x + 1 x y – 2 – 3 – 1 linear 0 1 1 3 2 5

8 -1 Graphing Linear Equations Check It Out: Example 1 A Continued

8 -1 Graphing Linear Equations Check It Out: Example 1 B Graph each equation and tell whether it is linear. y = x 2 + 1 x y – 2 5 – 1 2 0 1 non linear 1 2 2 5

8 -1 Graphing Linear Equations Check It Out: Example 1 B Continued

8 -1 Graphing Linear Equations A rate of change is a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable. The rates for a set of data may vary, or they may be constant.

8 -1 Graphing Linear Equations Additional Example 2 A: Identifying Constant and Variable Rates of Change in Data Determine whether the rates of change are constant or variable. +1 x y 0 0 1 2 +2 +4 3 6 +3 5 8 10 16 +4 Find the difference between consecutive data points. +6 Find each ratio of change in y to change in x. 2 =2 1 4 =2 2 6 =2 3 The rates of change are constant.

8 -1 Graphing Linear Equations Additional Example 2 B: Identifying Constant and Variable Rates of Change in Data Determine whether the rates of change are constant or variable. +2 x y 1 0 3 2 +2 +2 +1 +4 4 6 +0 +3 6 6 9 3 Find the difference between consecutive data points. +3 Find each ratio of change in y to change in x. 2 4 0 3 =1 =4 =0 =1 2 3 The rates of change are variable.

8 -1 Graphing Linear Equations Check It Out: Example 2 A Determine whether the rates of change are constant or variable. x y 0 1 1 3 2 5 3 7 4 9 The rates of change are constant.

8 -1 Graphing Linear Equations Check It Out: Example 2 B Determine whether the rates of change are constant or variable. x y – 2 – 1 0 – 3 – 4 – 3 2 0 The rates of change are variable.

8 -1 Graphing Linear Equations Additional Example 3: Sports Application A lift on a ski slope rises according to the equation a = 130 t + 6250, where a is the altitude in feet and t is the number of minutes that a skier has been on the lift. Five friends are on the lift. What is the altitude of each person if they have been on the ski lift for the times listed in the table? Draw a graph that represents the relationship between the time on the lift and the altitude.

8 -1 Graphing Linear Equations Additional Example 3 Continued

8 -1 Graphing Linear Equations Additional Example 3 Continued

8 -1 Graphing Linear Equations Additional Example 3 Continued The altitudes are: Anna, 6770 feet; Tracy, 6640 feet; Kwani, 6510 feet; Tony, 6445 feet; George, 6380 feet. This is a linear equation because when t increases by 1 unit, a increases by 130 units. Note that a skier with 0 time on the lift implies that the bottom of the lift is at an altitude of 6250 feet.

8 -1 Graphing Linear Equations Check It Out: Example 3 A home improvement store charges a base fee of $150 , plus $25 for each hour of machinery rental. The cost C for h hours is given by C = 25 h + 150. Find the cost for 1, 2, 3, 4, and 5 hours. Is this a linear equation? Draw a graph that represents the relationship between the cost and the number of hours of rental. 1 hr = $175, 2 hr = $200, 3 hr = $225 4 hr = $250, 5 hr = $275; linear

8 -1 Graphing Linear Equations Check It Out: Example 3 Continued

8 -1 Graphing Linear Equations Lesson Quizzes Standard Lesson Quiz for Student Response Systems

8 -1 Graphing Linear Equations Lesson Quiz Graph each equation and tell whether it is linear. 1. y = 3 x – 1 yes 1 x yes 4 3. y = x 2 – 3 no 2. y =

8 -1 Graphing Linear Equations Lesson Quiz for Student Response Systems 1. Identify the graph of the equation y = 4 x – 1 and tell whether it is linear. A. yes B. yes

8 -1 Graphing Linear Equations Lesson Quiz for Student Response Systems 2. Identify the graph of the equation tell whether it is linear. A. yes B. yes and

8 -1 Graphing Linear Equations Lesson Quiz for Student Response Systems 3. Identify the graph of the equation y = x 2 – 9 and tell whether it is linear. A. no B. no