1. Graphing Linear Equations

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

3. Any ordered pair of numbers that makes a linear equation true.
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. Find solutions using table
Graphing
Step 2:
Find solutions using table
y = x + 3
X | Y 1 2

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

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

9. Graph using a table (3 point method)
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. Where the line crosses the y-axis
Y-intercept
Where the line crosses the y-axis

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

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

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

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

19. Describes the steepness of a line
Slope
Describes the steepness of a line

20. Slope
Equal to:
Rise
Run

21. The change vertically, the change in y
Rise
The change vertically, the change in y

22. The change horizontally or the change in x
Run
The change horizontally or the change in x

23. Finding Slope Step 1: Find 2 points on a line (2, 3) (5, 4)
(2, 3) (5, 4)
(x1, y1) (x2, y2)

24. Find the RISE between these 2 points
Finding Slope
Step 2:
Find the RISE between these 2 points
Y2 - Y1 =
4 - 3 = 1

25. Find the RUN between these 2 points
Finding Slope
Step 3:
Find the RUN between these 2 points
X2 - X1 =
5 - 2 = 3

26. Write the RISE over RUN as a ratio
Finding Slope
Step 4:
Write the RISE over RUN as a ratio
Y2 - Y1 = 1
X2 - X

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

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

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

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

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