1. Graphs & Linear EquationsY
y=mx+b X

2. A Point (X,Y) (4,3) • (X,Y) is called an Ordered Pair Y X
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

3. How to Graph a Point Y (X,Y) (4,2) • 321 X -4-3-2-1 0 1 2 3 4
X is the distance along the x=axis
Y is the distance along the y=axis Y
3210
HINT: Think of the x-axis as the Number Line X -1 -2
HINT: Think of the y-axis a vertical Number Line

4. Important Vocabulary for Graphs
The Graph itself is called the x-y plane (ie. Plane surface) or The Coordinate Plane or Cartesian Coordinate Plane after Renee Descartes Y
y-axis
2nd Quadrant
1st Quadrant
(+X,+Y)
(-X,+Y) X
x-axis
(-X,-Y)
(+X,-Y)
3rd Quadrant
4th Quadrant
Quadrants start with Positive X & Y and go Counter Clockwise

5. 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.

6. RECALL X-Domain & Y-Range
Graphing Lines is just like finding the Range of 3 Domain Points: (Substitute each Domain value into the equation)
y = 2x-7 when the Domain is {-2, 0, 2}
f(-2) = 2•(-2) -7 = = (-2,-11)
f(0) = 2•(0) -7 = 0 -7 = (0,-7)
f(2) = 2•(2) -7 = 4 -7 = (2,-3)
Answer: RANGE: {-11, -7, -3}

7. Practice Finding 3 Points Given 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)

8. Sample Solutions
x y = 5x
0 0 5 10
x y = 4x-5
x y = 3x+1

9. Now Graph the 3 Points
x y = 5x
0 0 5 10 •
(2,10) •
(1,5) •
(0,0)

10. What is Intercept in Math?Y X
An Intercept is the coordinate where a line crosses the x or y axis

11. Using X&Y Intercepts to Graph a Line
y-axis
The Y intercept is the y coordinate (where a line crosses the y axis). •
(0,2) •
(3,0) X
x-axis
The X intercept is the x coordinate (where a line crosses the x axis).

12. Name the X&Y Intercepts
y-axis •
(0,2) •
(3,0) X
x-axis

13. Name the X&Y Intercepts
y-axis •
(0,2) • X
x-axis
(-2,0)

14. Name the X&Y Intercepts
y-axis X
x-axis

15. Name the X&Y Intercepts
y-axis X
x-axis

16. What is the value of x at the y intercept
What is the value of x at the y intercept? What is the value of Y at the x-intercept? Y
y-axis X
x-axis

17. 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)

18. Find the x- and y-intercepts. 2. -3x + 5y = 9
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, )

19. What is the x-intercept of 3x – 4y = 24?
(3, 0)
(8, 0)
(0, -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

20. What is the y-intercept of -x + 2y = 8?
(-1, 0)
(-8, 0)
(0, 2)
(0, 4) 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

21. Graph y = 2x - 6 using x&y intercepts
Graph Linear Eq.
Graph y = 2x - 6 using x&y intercepts
X Y = 2x - 6
1st Make x-y table Y
y-axis X
x-axis

22. Graph y = 2x - 6 using x&y intercepts
Graph Linear Eq.
Graph y = 2x - 6 using x&y intercepts
X Y = 2x - 6
0 -6
1st Make x-y table
2nd Set x = 0 and solve for y Y
y-axis X
x-axis
• (0,-6)

23. Graph y = 2x - 6 using x&y intercepts
Graph Linear Eq.
Graph y = 2x - 6 using x&y intercepts
X Y = 2x - 6
0 -6
1st Make x-y table
2nd Set x = 0 and solve for y
3rd Set y = 0 and solve for x Y
y-axis
• (3,0) X
x-axis
• (0,-6)

24. Graph y = 2x - 6 using x&y intercepts
Graph Linear Eq.
Graph y = 2x - 6 using x&y intercepts
X Y = 2x - 6
0 -6
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 Y
y-axis
• (3,0) X
x-axis
• (0,-6)

25. Graph y = 2x - 6 using x&y intercepts
Graph Linear Eq.
Graph y = 2x - 6 using x&y intercepts
X Y = 2x - 6
0 -6
4 2
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 Y
y-axis
• (4,2)
• (3,0) X
x-axis
• (0,-6)

26. Graphing Horizontal & Vertical Lines
This line has a y value of 4 for any x-value. It’s equation is y = 4 (meaning y always equals 4) Y
y-axis X
x-axis

27. Graphing Horizontal & Vertical Lines
This line has a x value of 1 for any y-value. It’s equation is x = 1 (meaning x always equals 1) Y
y-axis X
x-axis

28. The Equation of a Vertical Line is X=ConstantY
y-axis
x = 1 X
x-axis

29. The Equation of a Horizontal Line is Y=Constant
y-axis
y = 3 X
x-axis

30. Graph the following lines
Y = -4
Y = 2
X = 5
X = -5
X = 0
Y = 0

31. Answers
x = -5
x = 5 Y
y-axis X
x-axis

32. Answers Y
y-axis
y = 2 X
x-axis
y = -4

33. Answers Y
y-axis
y = 0 X
x-axis
x = 0