1. 2.4 Linear Functions: Graphs and Slope

2. 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
SLOPE IS ALSO CALLED AS THE RATE OF CHANGE

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

4. Y –intercept shows whether the graph shifted up or down
Example:
Y = 2x
Y = 2x + 5
Y = 2x – 3

5. Slope – intercept form
y = mx + b
m is the slope, b is the y-intercept

6. Find the slopes and the y-intercepts
y = ½ x + 4
5x – 4y = 8

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

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