FCP 10
6.1 Slope of a Line
A line segment or linear function has a special property referred to as slope. The slope
of a line tells you how steeply it rises and its sign tells you the direction of the line.
Slope is found by taking two points along the line and finding the differences between yvalues and the x-values. These differences are then placed in a ratio like below:
Slope = _vertical change_
horizontal change
= rise
run
These equations each reflect that the change in vertical distance gets divided by the
change in horizontal distance.
Example 1
Find the slope of the following line segments
As mentioned above, the slope of a line can be positive or negative. This will tell you what
direction the line rises in as it is tracked from left to right.
POSTITIVE SLOPE: Rises from left to right
NEGATIVE SLOPE: Falls from left to right
y
y
x
x
POSITIVE SLOPE
NEGATIVE SLOPE
There are two special types of lines that have special slopes: horizontal lines and
vertical lines. Determine what the slope would be for each of the following:
y
y
x
x
The slope of a horizontal line is __________ and the slope of a vertical line is
____________.
To draw the graph of a line, you need one of these two sets of information:
1) 2 different points
2) 1 point and the slope of the line
If you have 1 point and the slope, you start at the given point and count off the
appropriate number of units up and left/right as given by the slope to find another point
that you can connect.
Example 2
Determine whether each of the following lines has a positive or a negative slope.
y
x
Example 3
Draw a line segment, starting at the given point, with each given slope.
7
a) (-2, -3) slope =
b) (-4, 3) slope =
5
3
8
If you do not have a graph you can still find the slope of a line using any two of its
points. The formula is below, where (x1, y1), (x2, y2) are the two points from the line.
NOTE: It doesn’t matter which point is used for
x2 , y2
x1 , y1
and which is used for
as long as you are consistent.
Example 4
Using the formula, determine the slope for each pair of points.
a) (4, 8), (9, 8)
c) (-1, -1), (3, 7)
Example 5
Find the slope of the following data below.
Time Distance
(s)
(m)
1
10
2
15
3
20
4
25
5
30
6
35
7
40
Time Temperature
(s)
( C)
0
16
10
14
20
12
30
10
Example 6
Yvonne recorded the distances she had travelled at certain times since she began her
cycling trip along the Trans Canada Trail in Manitoba, from North Winnipeg to Grand
Beach. She plotted these data on a grid.
a) What is the slope of the line through these points?
b) What does the slope represent?
c) How can the answer to part b be used to determine:
i) how far Yvonne travelled in 1.75 hours?
ii) the time it took Yvonne to travel 55 km?