3.3 Slope

• 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 – y1 y1 – y2

x2 – x1 x1 – x2

m = =

= or

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

Find the slope of the line that goes through these 2 points

1) (1,5); (2,7)

2) (2,3); (1,3)

• 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

• 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

• Find the slopes and the y-intercepts1) y = ½ x + 4Slope is ½ and y-intercept is 42) 5x – 4y = 8 -4y = -5x + 8 y = 5/4 x - 2Slope is 5/4 and y-intercept is -2

• 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

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

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

More problems

1) Y = (1/2)x – 3

More problems

2) Y = (-3/4)x + 1

More problems

3) Y = -2x - 2