1. Graphing Linear Equations

2. Chapter Sections
7.1 – The Cartesian Coordinate System and Linear Equations in Two Variables
7.2 – Graphing Linear Equations
7.3 – Slope of a Line
7.4 – Slope-Intercept and Point-Slope Forms of a Linear Equation
7.5 – Graphing Linear Inequalities
7.6 – Functions
Chapter 1 Outline

3. Slope of a Line

4. Consider the points (3, 6) and (1,2).
Slope
The slope of a line is the ratio of the vertical change, or rise, to the horizontal change, or run, between any two selected points on the line.
Consider the points (3, 6) and (1,2).

5. Slope
(3, 6) and (1,2)
This means the graph is moving up 4 and to the right 2.
Horizontal Change
Vertical Change

6. Slope
Simplifying, , so m = 2
Horizontal Change
Vertical Change
m = 2

7. Positive & Negative Slopesx y x y
Positive Slope
Negative Slope
Line rises from left to right
Line falls from left to right

8. Every horizontal like has a slope of 0.
Horizontal Lines
Every horizontal like has a slope of 0.
x = 2

9. The slope of any vertical line is undefined.
Vertical Lines
The slope of any vertical line is undefined.
y = -4

10. Parallel Lines
Two non-vertical lines with the same slope and different y-intercepts are parallel . Any two vertical lines are parallel to each other.
m1 = m2

11. Perpendicular Lines -1 m1 = m2
Two lines whose slopes are negative reciprocals of each other are perpendicular lines. Any vertical line is perpendicular to any horizontal line.
m1 = m2 -1