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Chapter 2
Graphing and Writing Linear Equations
2.1 Graphing Linear Equations
Linear Equation
• An equation whose graph is a straight line.
• Anything with x to the first power
Solutions
• The points on the line
• Make the equation true
Determine if the ordered pair is a solution of the equation.
y = 2x + 1
(3 , 7 )
7 = 2(3) + 1YES
The ordered pair (3,7) is a solution.
Making a Table to Graph1. Solve for y: y=mx+b
2 . A. Pick your x values (-1, 0,1)
B. If “m” is a fraction and “b” is not then pick the + and – version of the denominator and 0 as your x -values
3. Plug in the x values into the equation to find the corresponding y values
4. Plot the (x, y) ordered pairs on the coordinate plane and draw a line
8
6
4
2
-2
-4
-6
-8
-10 -5 5 10 x
yFind 3 solutions
y = 2x + 1
X Values Y=2x + 1 Y Values (x,y)
1
0
-1
2(1) +1 3 (1,3)
2(0) +1 1 (0,1)
2(-1) +1 -1 (-1,-1)
8
6
4
2
-2
-4
-6
-8
-10 -5 5 10 x
yGraph:
x Y=2/3x +5 y (x,y)
3
0
-3
(2/3)(3) +5 7 (3,7)
(2/3) (0) +5 5 (0,5)
(2/3)(-3)+5 3 (-3,3)
25
3y x
Solve for ‘y’9 3 20x y
Solve for ‘y’ means “get y all by itself”
9x 9x3 9 20x y
203
3x y
3 3 3
8
6
4
2
-2
-4
-6
-8
-10 -5 5 10 x
yGraph:
-2x + y = 5y = 2x + 5
X Y=2x +5 Y (x,y)
1
0
-1
2(1) +5 7 (1,7)
2(0) +5 5 (0,5)
2(-1)+5 3 (-1,3)
Types of Linear Lines
• Diagonal: when there are two variables
• Vertical: when there is only x
• Horizontal: when there is only y
Horizontal and Vertical Lines
• The graph of y= # is HORIZONTAL
• The graph x =# is VERTICAL
6
5
4
3
2
1
-1
-2
-3
-4
-5
-8 -6 -4 -2 2 4 6 8
Graph y = 4 using 3-points
x y
036
6
5
4
3
2
1
-1
-2
-3
-4
-5
-8 -6 -4 -2 2 4 6 8
Graph x = 6 using 3-points
x y
03
- 4
Homework
TB: Page 46 (2-18 even, 20-23 all, 24-32 even