12-1 Graphing Linear Equations Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Warm Up Solve each equation for y. 1. 6y – 12x = – 2y – 4x = y – 5x = y + 6x = 18 y = 2x + 4 y = – 2x – 10 Course Graphing Linear Equations y = – 2x + 6 y = x

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 Course Graphing Linear Equations

Learn to identify and graph linear equations. Course Graphing Linear Equations

Vocabulary linear equation Insert Lesson Title Here Course 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. To find a solution that lies between two points (x 1, y 1 ) and (x 2, y 2 ), choose an x-value between x 1 and x 2 and find the corresponding y-value. Course Graphing Linear Equations

Insert Lesson Title Here Read x 1 as “x sub one” or “x one.” Reading Math Course 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 Course Graphing Linear Equations

Graph the equation and tell whether it is linear. y = 3x – 1 Additional Example 1A: Graphing Equations x3x – 1y(x, y) –2 – –73(–2) – 1 3(–1) – 1 3(0) – 1 3(1) – 1 3(2) – 1 –4 –1 2 5 (–2, –7) (–1, –4) (0, –1) (1, 2) (2, 5) Course Graphing Linear Equations

Additional Example 1A Continued The equation y = 3x – 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. Course Graphing Linear Equations

Insert Lesson Title Here Be careful when graphing each ordered pair. Double check each point you plot. Caution! Course Graphing Linear Equations

Graph the equation and tell whether it is linear. y = x 3 Additional Example 1B: Graphing Equations xx3x3 y(x, y) –2 – –8(–2) 3 (–1) 3 (0) 3 (1) 3 (2) 3 – (–2, –8) (–1, –1) (0, 0) (1, 1) (2, 8) Course Graphing Linear Equations

Additional Example 1B Continued The equation y = x 3 is not a linear equation because its graph is not a straight line. Also notice that as x increases by a constant of 1 unit, the change in y is not constant. x–2–2–1–1012 y–8–8–1– Course Graphing Linear Equations

Additional Example 1C: Graphing Equations Graph the equation and tell whether it is linear. y = – 3x3x 4 Course Graphing Linear Equations

Additional Example 1 Continued The equation y = – is a linear equation because the points form a straight line. Each time the value of x increases by 1, the value of y decreases by or y decreases by 3 each time x increases by 4. 3x3x Course Graphing Linear Equations

Graph the equation and tell whether it is linear. y = 2 Additional Example 1D: Graphing Equations For any value of x, y = 2. x2y(x, y) –2 – (–2, 2) (–1, 2) (0, 2) (1, 2) (2, 2) Course Graphing Linear Equations

Additional Example 1D Continued The equation y = 2 is a linear equation because the points form a straight line. As the value of x increases, the value of y has a constant change of 0. Course Graphing Linear Equations

Graph the equation and tell whether it is linear. y = 2x + 1 Check it Out: Example 1A x2x + 1y(x, y) –4 – –72(–4) + 1 2(–2) + 1 2(0) + 1 2(2) + 1 2(4) + 1 – (–4, –7) (–2, –3) (0, 1) (2, 5) (4, 9) Course Graphing Linear Equations

Check It Out: Example 1A Continued The equation y = 2x + 1 is linear equation because it is the graph of a straight line and each time x increase by 1 unit, y increases by 2 units. Course Graphing Linear Equations

Graphing the equation and tell whether it is linear. y = x 2 Check It Out: Example 1B xx2x2 y(x, y) –2 – (–2) (–2, 4) (–1, 1) (0, 0) (1, 1) (2, 4) (–1) 2 (0) 2 (1) 2 (2) 2 Course Graphing Linear Equations

Check It Out: Example 1B Continued The equation y = x 2 is not a linear equation because its graph is not a straight line. Course Graphing Linear Equations

Check It Out: Example 1C Graph the equation and tell whether it is linear. y = x xy(x, y) –8 – –8 – (–8, –8) (–6, –6) (0, 0) (4, 4) (8, 8) Course Graphing Linear Equations

Check It Out: Example 1C Continued The equation y = x is a linear equation because the points form a straight line. Each time the value of x increases by 1, the value of y increases by 1. Course Graphing Linear Equations

Check It Out: Example 1D For any value of x, y = 7. Graph the equation and tell whether it is linear. D. y = 7 x7y(x, y) –8 – (–8, 7) (–4, 7) (0, 7) (4, 7) (8, 7) Course Graphing Linear Equations

Check It Out: Example 1D Continued The equation y = 7 is a linear equation because the points form a straight line. As the value of x increases, the value of y has a constant change of 0. Course Graphing Linear Equations

Additional Example 2: Sports Application A lift on a ski slope rises according to the equation a = 130t , 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. Course Graphing Linear Equations

Additional Example 2 Continued Course Graphing Linear Equations

Additional Example 2 Continued Course Graphing Linear Equations

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. Additional Example 2 Continued Course Graphing Linear Equations

Check It Out: Example 2 In an amusement park ride, a car travels according to the equation D = 1250t where t is time in minutes and D is the distance in feet the car travels. Below is a chart of the time that three people have been in the cars. Graph the relationship between time and distance. How far has each person traveled? RiderTime Ryan1 min Greg2 min Colette3 min Course Graphing Linear Equations

Check It Out: Example 2 Continued tD =1250tD(t, D) 11250(1)1250(1, 1250) 21250(2)2500(2, 2500) 31250(3)3750(3, 3750) Course Graphing Linear Equations The distances are: Ryan, 1250 ft; Greg, 2500 ft; and Collette, 3750 ft.

Check It Out: Example 2 Continued x y This is a linear equation because when t increases by 1 unit, D increases by 1250 units Time (min) Distance (ft) Course Graphing Linear Equations

Lesson Quiz Graph each equation and tell whether it is linear. 1. y = 3x – 1 2. y = x 3. y = x 2 – 3 yes Insert Lesson Title Here no 1414 Course Graphing Linear Equations