1. SLOPE
Objectives:
Find the slope of a line given the coordinates of two points on the line
Graph equations using y=mx+b form.

2. What is Slope? Change in Y Change in X Steepness Rise Run
Y=mx + b
Amount of Slant

3. The Graph of y = mx +b Consider the graph of y = x - 2 y5 4 3 2 1 -2 -3 -4 -5 y x
Compare to the graph
of y = ½x - 2
Compare to the graph
of y=2x-2

4. The Graph of y = mx +b Consider the graph of y = x - 2 y5 4 3 2 1 -2 -3 -4 -5 y x
Compare to the graph
of y = -1x - 2
Compare to the graph
of y = -2x - 2

5. Determining Slope Rise=1 Rise=12 Run =2 Run =4 Rise=6 Run =2 Slope=

6. Determining Slope Rise= 8 = -2 Rise= 0 Run = -4 1 Run = n Rise= -2

7. Determining Slope
Rise= n
Run = 0
The Slope is UNDEFINED

8. Determining Slope 5-(-6) = 11 6 2-(-4)
Find the change in the Y-coordinates by subtracting(rise)
Pick 2 points on the line
(2, 5)
Find the change in the X-coordinates by subtracting(run)
5-(-6)
= 11 6
(-4, -6)
2-(-4)
Write as a ratio (rise/run)

9. Determining Slope Y1-Y2 Y2-Y1 m = X1-X2 X2-X1
In general, to find the slope given two points on a line:
Subtract the Y-coordinates (rise)
(x1, y1)
Subtract the X-coordinates (run)
Write as a ratio (rise/run)
(x2, y2)
Y1-Y2
X1-X2
Y2-Y1
m = =
X2-X1

10. Slope Summary Positive Slope Slope = 0 Undefined Slope Negative Slope
Negative slope is a downer
Negative Slope

11. Linear Equations (y = mx + b)
b = y-intercept
plot (0,b) to get your first point
m = slope
written as a fraction slope = rise/run
Lean up and to the right if positive
Lean down and to the right if negative