The document discusses key concepts related to graphing lines including: 1) Horizontal and vertical lines can be represented by equations in the form of y=a constant or x=a constant. 2) The slope of a line represents the steepness and is calculated by rise over run using two points. 3) Lines can have positive, negative, zero or undefined slopes depending on their angle and direction. 4) Parallel lines have the same slope while perpendicular lines have slopes that are negative reciprocals of each other.

1. Graphs & Linear Equations Y X y=mx+b

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

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

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

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

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

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

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

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

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

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

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

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

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

15. Switch points and calculate slope Make (3,2) (x 2 ,y 2 ) & (6,4) (x 1 ,y 1 ) • • (x 2 ,y 2 )(6’4) (x 1 ,y 1 )(3,2) • • (x 1 ,y 1 )(6,4) (x 2 ,y 2 )(3,2)

16. Recalculation with points switched • • (x 1 ,y 1 )(6,4) (x 2 ,y 2 )(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 x 1 ,y 1 ,x 2 ,y 2 over numbers 2nd Step: Write Formula and Substitute x 1 ,x 2 ,y 1 ,y 2 values. 3rd Step: Calculate & Simplify (3,4) & (-2,6) x 1 y 1 x 2 y 2

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

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

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 x 1 ,x 2 ,y 1 ,y 2 over numbers 2nd Step: Write Formula and Substitute x 1 ,x 2 ,y 1 ,y 2 values. 3rd Step: Calculate & Simplify NOTE: Be Neat, Careful, and Precise and Check your work as you go..

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

25. ZERO Slope Horizontal NO Slope Vertical Drop

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

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