1. 3.3 Slope

2. A line with positive slope slants up from left to right
A line with negative slopes slants downward from left to right
The larger the slope, the steeper the slant
Slope is the steepness of the line (the slant of the line) and is defined by
rise the change in y
run the change in x
y2 – y y1 – y2
x2 – x x1 – x2 =
m = = or

3. Find the slope of the line that goes through these 2 points
(1,5); (2,7)
(2,3); (1,3)

4. m is the slope, b is the y-intercept * Slope of a horizontal line is 0
Slope – intercept form
y = mx + b
m is the slope, b is the y-intercept
* Slope of a horizontal line is 0
Example: y = 5
* Slope of a vertical line is undefined
Example: x = 3

5. Y –intercept shows whether the graph shifted up or down
Examples:
Y = 2x
Y = 2x + 5 Move up 5 units
Y = 2x – 3 Move down 3 units

6. Find the slopes and the y-intercepts
y = ½ x + 4
Slope is ½ and y-intercept is 4
5x – 4y = 8
-4y = -5x + 8
y = 5/4 x - 2
Slope is 5/4 and y-intercept is -2

7. Find the linear equation if you know slope m = 3 and y-intercept is (0,4)
We have y =mx + b
So y = 3x + 4

8. Graphing using slopes and y-intercepts
Start by plotting y-intercept (0,b)
From there, use the slope = rise / run
If +, go up, or right
If - , go down or left

9. Y = 3x + 2
Step 1: Start with the y-intercept (0,2)
Step 2: Slope is 3/1 so we rise 3 (up 3) and run 1 (to the right 1)
Step 3: Connect 2 points, we will have the function y = 3x - 2

10. More problems
Y = (1/2)x – 3

11. More problems
2) Y = (-3/4)x + 1

12. More problems
3) Y = -2x - 2