1. Graphing Linear Equations

2. Linear Equation An equation for which the graph is a line

3. Solution Any ordered pair of numbers that makes a linear equation true. (9,0) IS ONE SOLUTION FOR Y = X - 9

4. Linear Equation Example: y = x + 3

5. Graphing Step 1: ~ Three Point Method ~ Choose 3 values for x

6. Graphing Step 2: Find solutions using table y = x + 3 X | Y 0 1 2

7. Graphing Step 3: Graph the points from the table (0,3) (1,4) (2,5)

8. Graphing Step 4: Draw a line to connect them

9. Try These Graph using a table (3 point method) 1) y = x + 3 2) y = x - 4

10. Slope-Intercept y = mx + b m = slope b = y-intercept

11. Slope-Intercept The m in the slope-intercept form is ALWAYS attached to the X variable. The slope is NEVER including the X variable For example, if given y = 3x + 4 the slope is 3 NOT 3x.

12. Y-intercept Where the line crosses the y-axis

13. Y-intercept The y-intercept has an x-coordinate of ZERO

14. Y-intercept To find the y- intercept, plug in ZERO for x and solve

15. Y-Intercept Summary The y-intercept is the b in the slope intercept form. This b (y-intercept) is your starting point on the graph. –To easily remember this, think of b as you Beginning point. For example, in y = 3x + 4 the Beginning point is at (0,4) {Remember: to find the y- intercept, plug on zero for the x.}

16. X-intercept Where the line crosses the x-axis

17. X-intercept The x-intercept has a y coordinate of ZERO

18. X-intercept To find the x- intercept, plug in ZERO for y and solve

19. Slope Describes the steepness of a line

20. Slope Equal to: Rise Run

21. Rise The change vertically, the change in y

22. Run The change horizontally or the change in x

23. Finding Slope Step 1: Find 2 points on a line (2, 3) (5, 4) (x 1, y 1 ) (x 2, y 2 )

24. Finding Slope Step 2: Find the RISE between these 2 points Y 2 - Y 1 = 4 - 3 = 1

25. Finding Slope Step 3: Find the RUN between these 2 points X 2 - X 1 = 5 - 2 = 3

26. Finding Slope Step 4: Write the RISE over RUN as a ratio Y 2 - Y 1 = 1 X 2 - X 1 3

27. Step 1: Mark a point on the y-intercept

28. Step 2: Define slope as a fraction...

29. Step 3: Numerator is the vertical change (RISE)

30. Step 4: Denominator is the horizontal change (RUN)

31. Step 5: Graph at least 3 points and connect the dots