12-1 graphing linear equations course 3 warm up warm up problem of the day problem of the day lesson...
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12-1 Graphing Linear Equations
Course 3
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm UpSolve each equation for y.
1. 6y – 12x = 24
2. –2y – 4x = 20
3. 2y – 5x = 16
4. 3y + 6x = 18
y = 2x + 4
y = –2x – 10
Course 3
12-1 Graphing Linear Equations
y = –2x + 6
y = x + 852
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 3
12-1 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. To find a solution that lies between two points (x1, y1) and (x2, y2), choose an x-value between x1 and x2 and find the corresponding y-value.
Course 3
12-1 Graphing Linear Equations
Insert Lesson Title Here
Read x1 as “x sub one” or “x one.”
Reading Math
Course 3
12-1 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.
3
3
3
2
2
2
Course 3
12-1 Graphing Linear Equations
Graph the equation and tell whether it is linear.
y = 3x – 1
Additional Example 1A: Graphing Equations
x 3x – 1 y (x, y)
–2
–1
0
1
2
–73(–2) – 13(–1) – 1
3(0) – 13(1) – 1
3(2) – 1
–4
–1
2
5
(–2, –7)
(–1, –4)(0, –1)
(1, 2)(2, 5)
Course 3
12-1 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 3
12-1 Graphing Linear Equations
Insert Lesson Title Here
Be careful when graphing each ordered pair. Double check each point you plot.
Caution!
Course 3
12-1 Graphing Linear Equations
Graph the equation and tell whether it is linear.
y = x3
Additional Example 1B: Graphing Equations
x x3 y (x, y)
–2
–1
0
1
2
–8(–2)3
(–1)3
(0)3
(1)3
(2)3
–1
0
1
8
(–2, –8)
(–1, –1)(0, 0)
(1, 1)(2, 8)
Course 3
12-1 Graphing Linear Equations
Additional Example 1B Continued
The equation y = x3 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 –1 0 1 2
y –8 –1 0 1 8
+7 +1 +1 +7Course 3
12-1 Graphing Linear Equations
Additional Example 1C: Graphing EquationsGraph the equation and tell whether it is linear.
y = – 3x4
Course 3
12-1 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.
3x4
34
Course 3
12-1 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.
x 2 y (x, y)
–2
–1
0
1
2
222
2
2
2
2
2
2
2
(–2, 2)
(–1, 2)(0, 2)
(1, 2)(2, 2)
Course 3
12-1 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 3
12-1 Graphing Linear Equations
Graph the equation and tell whether it is linear.
y = 2x + 1
Check it Out: Example 1A
x 2x + 1 y (x, y)
–4
–2
0
2
4
–72(–4) + 12(–2) + 1
2(0) + 12(2) + 1
2(4) + 1
–3
1
5
9
(–4, –7)
(–2, –3)(0, 1)
(2, 5)(4, 9)
Course 3
12-1 Graphing Linear Equations
Check It Out: Example 1A Continued
The equation y = 2x + 1is 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 3
12-1 Graphing Linear Equations
Graphing the equation and tell whether it is linear.
y = x2
Check It Out: Example 1B
x x2 y (x, y)
–2
–1
0
1
2
4(–2)2
1
0
1
4
(–2, 4)
(–1, 1)(0, 0)
(1, 1)(2, 4)
(–1)2
(0)2
(1)2
(2)2
Course 3
12-1 Graphing Linear Equations
Check It Out: Example 1B Continued
The equation y = x2 is not a linear equation because its graph is not a straight line.
Course 3
12-1 Graphing Linear Equations
Check It Out: Example 1C
Graph the equation and tell whether it is linear.
y = x
x y (x, y)
–8
–6
0
4
8
–8
–6
0
4
8
(–8, –8)
(–6, –6)(0, 0)
(4, 4)(8, 8)
Course 3
12-1 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 3
12-1 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
x 7 y (x, y)
–8
–4
0
4
8
777
7
7
7
7
7
7
7
(–8, 7)
(–4, 7)(0, 7)
(4, 7)(8, 7)
Course 3
12-1 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 3
12-1 Graphing Linear Equations
Additional Example 2: Sports Application
A lift on a ski slope rises according to the equation a = 130t + 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.
Course 3
12-1 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 3
12-1 Graphing Linear Equations
Check It Out: Example 2In 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?
Rider Time
Ryan 1 min
Greg 2 min
Colette 3 min
Course 3
12-1 Graphing Linear Equations
Check It Out: Example 2 Continued
t D =1250t D (t, D)
1 1250(1) 1250 (1, 1250)
2 1250(2) 2500 (2, 2500)
3 1250(3) 3750 (3, 3750)
Course 3
12-1 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.
1250
2500
1 2
3750
5000
3 4Time (min)
Dis
tan
ce (
ft)
Course 3
12-1 Graphing Linear Equations