Math 95 Notes
Section 3.3
Slope of a line and Rate of Change
Objective:
Students will be able to:
 Compute the slope of a line given two points
 Determine if lines are parallel, perpendicular, or neither.
Slope of a line represents the ratio of the change in y over the change in x.
Notation: m
Formula:
rise
m
looking at it in term of a graph
run
y y
m  2 1 Use this when you are given two points
x2  x1
How slope looks when you graph a line.
Positive Slope: The line will be leaning to the right.
Negative Slope: The line leans to the left.
Slope of Zero: The line is a horizontal line.
Undefined Slope: The line is a vertical line.
Example:
Determine the slope from the graph.
B Up 2 A Right 4 To find the slope, we need to identify two points on the line. You will see that I have
points A and B labeled. So we are going to how to move to get from A to B. To help with
the movement, we can put a right triangle under the line with the line being on the
hypotenuse. So we can see that we moved “right 4” unit and “up 2” unit. So the help us
find the slope, we use that the slope is the rise over the run. The rise is going up or
down or the height of the triangle, which is 2. The run is going left or right or the base of
the triangle, which is 4. So as a ratio m = 2/4 or m = ½.
Example:
Determine the slope of a line that passes through the given points.
a. (-5, 4) and (-11, 12)
y y
12  4
8
4
m 2 1 


x2  x1 11   5  6
3
b. (2, -7) and (2, 5)
y  y 5   7  12
m 2 1 

 undefined
22
0
x2  x1
c. (5, 3) and (-2, 3)
y y
33
0
m 2 1 

0
x2  x1 2  3 5
d. (-6, 5) and (-10, 4)
y y
45
1 1
m 2 1 


x2  x1 10   6  4 4
Parallel and Perpendicular Lines
If lines are parallel, they will have the same slope.
If lines are perpendicular, the lines will have a negative reciprocal slope.
Example:
2
m
3
2
m   Parallel lines have the same slope.
3
3
m  Perpendicular lines slopes are negative reciprocals.
2