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Graphs & Linear Equations
Y
X
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A PointY
X
(X,Y) is called an Ordered Pair
The X value or X Coordinate is the location of a point in the X direction
The Y value or Y Coordinate is the location of a point in the Y direction
(X,Y) (4,3) •
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How to Graph a PointY
X
(X,Y) (4,2) •
X is the distance along the x=axis
Y is the distance along the y=axis
1 2 3 4
321
HINT: Think of the x-axis as the Number Line
-4-3-2-1 0
X1 2 3 4-4-3-2-1 0
HINT: Think of the y-axis a vertical Number Line
Y
3210
-1-2
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Important Vocabulary for Graphs
Y
X
The Graph itself is called the x-y plane (ie. Plane surface) or The Coordinate Plane or Cartesian Coordinate Plane after Renee Descartes
(+X,+Y)
(+X,-Y)(-X,-Y)
(-X,+Y)
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Graphing Linear Equations(Find 3 Domain & Range Points)
First Degree Equations are Lines (y=mx+b) and you calculate 3 (X,Y) values
Make sure the points line up on a x-y graph and connect the dots.
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RECALL X-Domain & Y-Range
y = 2x-7 when the Domain is {-2, 0, 2}
f(-2) = 2•(-2) -7 = -4 -7 = -11 (-2,-11)f(0) = 2•(0) -7 = 0 -7 = -7 (0,-7)f(2) = 2•(2) -7 = 4 -7 = -3 (2,-3)
Answer: RANGE: {-11, -7, -3}
Graphing Lines is just like finding the Range of 3 Domain Points:(Substitute each Domain value into the equation)
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Practice Finding 3 PointsGiven a Linear Equation
Find any 3 (X,Y) points for the following equations:
y=5x
y=4x-5
y=3x+1
(Hint: Try x=0)
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Sample Solutions
x y = 5x
0 0
1 5
2 10
x y = 4x-5 x y = 3x+1
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Now Graph the 3 Pointsx y = 5x
0 0
1 5
2 10
•
•
•(0,0)
(1,5)
(2,10)
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What is Intercept in Math?Y
X
An Intercept is the coordinate where a line crosses the x or y axis
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Using X&Y Intercepts to Graph a Line
The X intercept is the x coordinate (where a line crosses the x axis).
Y
X
(0,2)
(3,0)
•
•
The Y intercept is the y coordinate (where a line crosses the y axis).
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Name the X&Y Intercepts
Y
X
(0,2)
(3,0)
•
•
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Name the X&Y Intercepts
Y
X
(0,2)
(-2,0)
•
•
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Name the X&Y Intercepts
Y
X
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Name the X&Y Intercepts
Y
X
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What is the value of x at the y intercept? What is the value of Y at the x-intercept?
Y
X
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Find the x- and y-intercepts.1. x - 2y = 12
x-intercept: Plug in 0 for y.
x - 2(0) = 12
x = 12; (12, 0)
y-intercept: Plug in 0 for x.
0 - 2y = 12
y = -6; (0, -6)
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x-intercept: Plug in 0 for y.
-3x - 5(0) = 9
-3x = 9
x = -3; (-3, 0)
y-intercept: Plug in 0 for x.
-3(0) + 5y = 9
5y = 9
y = ; (0, )9
5
9
5
Find the x- and y-intercepts.2. -3x + 5y = 9
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What is the x-intercept of3x – 4y = 24?
1. (3, 0)
2. (8, 0)
3. (0, -4)
4. (0, -6)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32
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What is the y-intercept of-x + 2y = 8?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32
1. (-1, 0)
2. (-8, 0)
3. (0, 2)
4. (0, 4)
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Graph y = 2x - 6 using x&y intercepts
1st Make x-y table
X Y = 2x - 6
Y
X
Graph Linear Eq.
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Graph y = 2x - 6 using x&y intercepts
1st Make x-y table
2nd Set x = 0 and solve for y
X Y = 2x - 6
0 -6
Y
X
• (0,-6)
Graph Linear Eq.
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Graph y = 2x - 6 using x&y intercepts
1st Make x-y table
2nd Set x = 0 and solve for y
3rd Set y = 0 and solve for x
X Y = 2x - 6
0 -6
3 0Y
X
• (0,-6)
• (3,0)
Graph Linear Eq.
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Graph y = 2x - 6 using x&y intercepts
1st Make x-y table
2nd Set x = 0 and solve for y
3rd Set y = 0 and solve for x
4th Plot these 2 points and draw line
X Y = 2x - 6
0 -6
3 0Y
X
• (0,-6)
• (3,0)
Graph Linear Eq.
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Graph y = 2x - 6 using x&y intercepts
1st Make x-y table
2nd Set x = 0 and solve for y
3rd Set y = 0 and solve for x
4th Plot these 2 points and draw line
5th Use 3rd point to check
X Y = 2x - 6
0 -6
3 0
4 2Y
X
• (0,-6)
• (3,0)
• (4,2)
Graph Linear Eq.
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Graphing Horizontal & Vertical Lines
Y
X
This line has a y value of 4 for any x-value. It’s equation is
y = 4 (meaning y always equals 4)
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Graphing Horizontal & Vertical Lines
Y
X
This line has a x value of 1 for any y-value. It’s equation is
x = 1 (meaning x always equals 1)
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The Equation of a Vertical Line is X=Constant
Y
X
x = 1
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The Equation of a Horizontal Line is Y=Constant
Y
X
y = 3
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Graph the following lines
Y = -4
Y = 2
X = 5
X = -5
X = 0
Y = 0
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Answers
Y
X
x = 5x = -5
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Answers
Y
X
y = -4
y = 2
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Answers
Y
X
x = 0
y = 0