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

2. 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

3. 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

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

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

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

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

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

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

10. SLOPE =
NEGATIVE-DOWN
POSITIVE-UP
Slope is a measure of STEEPNESS

11. Think of m for Mountain The Symbol for SLOPE = m NEG. Slope is -m
POS. Slope is +m
Think of m for Mountain

12. SLOPE = How much does this line rise? How much does it run? (6,4) 4 •3
(3,2) 2 • 1
(0,0) 1 2 3 4 5 6
How much does this line rise?
How much does it run?

13. SLOPE = 2 3 2 3 How much does this line rise? How much does it run?
(6,4) 4 • 3
(3,2) 2 • 1
(0,0) 1 2 3 4 5 6
How much does this line rise?
How much does it run? 2 3

14. m=SLOPE =
x2y2
(6,4) 4 •
x1y1 3
(3,2) 2 • 1
(0,0) 1 2 3 4 5 6

15. Switch points and calculate slope Make (3,2) (x2,y2) & (6,4) (x1,y1)• •
(x1,y1)(3,2)
(x2,y2)(3,2) • •

16. Recalculation with points switched
(x1,y1)(6,4) •
(x2,y2)(3,2) •
Same slope as before

17. It doesn’t matter what 2 points you choose on a line the slope must come out the same

18. Keeping Track of Signs When Finding The Slope Between 2 Points
• Be Neat & Careful
• Use (PARENTHASES)
• Double Check Your Work as you Go
• Follow 3 Steps

19. 3 Steps for finding the Slope of a line between 2 Points (3,4)&(-2,6)
1st Step: Write x1,y1,x2,y2 over numbers
2nd Step: Write Formula and Substitute x1,x2,y1,y2 values.
3rd Step: Calculate & Simplify
x1 y1
x2 y2
(3,4) & (-2,6)

20. Find the Slopes of Lines containing these 2 Points
1. (1,7) & (5,2)
2. (3,5) & (-2,-8)
3. (-3,-1) & (-5,-9)
4. (4,-2) & (-5,4)
5. (3,6) & (5,-5)
6. (1,-4) & (5,9)

21. ANSWERS
1. (1,7) & (5,2)
2. (3,5) & (-2,-8)
3. (-3,-1) & (-5,-9)
4. (4,-2) & (-5,4)
5. (3,6) & (5,-5)
6. (1,-4) & (5,9)

22. Solve for y if (9,y) & (-6,3) & m=2/3

23. Review Finding the Slopes of Lines Given 2 Points
1st Step: Write x1,x2,y1,y2 over numbers
2nd Step: Write Formula and Substitute x1,x2,y1,y2 values.
3rd Step: Calculate & Simplify
NOTE:
Be Neat, Careful, and Precise and Check your work as you go..

24. Negative Slope
Is Down the Hill
Positive Slope
Is Up the Hill
NO Slope
Vertical Drop
ZERO Slope Horizontal

25. NO Slope
Vertical Drop
ZERO Slope Horizontal

26. Parallel Lines Have the Same Slope5 4 • 3 2 • 1
(0,0) 1 2 3 4 5 6

27. Perpendicular Lines Have Neg. Reciprocal Slopes3 2 1
(0,0) 1 2 3 4 5 6