1. Section 3.3
The Slope of a Line

2. Slope
In a coordinate plane, the slope of a straight line is defined by the change in y divided by the change in x.
(3, 0) x y 1 2 3 4 1 2 3 4
(0, 2)
Change in y = 2
Change in x = 3

3. Definition of Slope of a Line
The slope of any nonvertical line that contains the points with coordinates (x1, y1) and (x2, y2) is defined by the difference ratio
where x2  x1.

4. Example
Find the slope of the line that passes through (3, 6) and (1, 2).

5. Example
Find the slope of the line that passes through (3, 2) and (2, 4).

6. Example
Find the slope of the line that passes through (0, 2) and (5, 2).

7. Example
Find the slope of the line that passes through (4, 0) and (4, 4).

8. Types of Slope Positive Slope Line goes up to the right yx y
1. Lines with positive slopes go upward as x increases. x y
Negative Slope
Line goes downward to the right
Lines with negative slopes go downward as x increases.

9. Types of Slope x y Zero Slope Horizontal Line
Horizontal lines have a slope of 0.
Undefined Slope
Vertical Line x y
A vertical line has an undefined slope.

10. Slope-Intercept
The slope-intercept form of the equation of a line that has slope m and y-intercept (0, b) is given by
y = mx + b.
y = 3x – 4
The slope is 3.
The y-intercept is (0, -4).
The slope is
The y-intercept is

11. Example
What is the slope and the y-intercept of the line 5x + 3y = 2? Solve the equation for y.
The y-intercept is (0, 2/3).
The slope is -5/3.

12. Example
Find the equation of the line with slope and y-intercept (0, 5).

13. Example Graph the line with slope and y-intercept (0, 2). 3 units down1 2 3 4 1 2 3 4
(0, 2)
3 units down
rise
2 units to the right
run
(2, 1)