Mathematics 1201
Unit 6: Linear Functions
Lesson 6.1: The Slope of a Line (2 classes)
In this lesson, we will be taking a look at the slope of a line. We will:
1.
2.
3.
4.
5.
6.
7.
Define the slope of a line.
Determine the slope of a line or line segment
Classify lines in a given set as having positive or negative slopes.
Explain the meaning of the slope of a horizontal or vertical line.
Draw a line segment with a given slope.
Given the coordinates of two points on a line, determine the slope of the lines.
Explain what the slope represents in a given situation.
Definition: Slope is a measure of how one quantity changes with respect to another. The slope of a line
is a measure of how much the y-coordinate changes with respect to the x-coordinate.
Example #1
Consider a line that has a slope of 3 (or ). This means that the y-coordinate increases by 3 when the xcoordinate increases by 1.
It could also be said that the y-coordinate decreases by 3 each time the x-coordinate decreases by 1.
Example #2
Consider a line that has a slope of -2 (or
). This means that the y-coordinate decreases by 2
when the x-coordinate increases by 1.
It could also be said that the y-coordinate increases by 2 each time the x-coordinate decreases by 1.
Example #3
Consider a line that has a slope of
(or
). This means that the y-coordinate decreases by 5 when the
x-coordinate increases by 3.
It could also be said that the y-coordinate increases by 5 when the x-coordinate decreases by 3.
Try question #7 on page 340 in the text.
Calculating the Slope of a Line
In Unit 5, you calculated the rate of change using the formula
. The slope of a line is also a
rate of change, so we can use this same formula to calculate the slope of a line!
The slope of a line can easily be calculated by doing the following:
1. Pick 2 points on the line. It may help to pick 2 points that you are able to determine the
coordinates for without having to estimate.
2. Determine the “rise” and “run” values on the graph.
3. Put both values into the slope formula!
The Slope of Horizontal and Vertical Lines
Slope of a Horizontal Line
Slope of Vertical Line
In summary,
1. The slope of a horizontal line will always be zero, as the rise is always zero.
2. The slope of a vertical line will always be undefined, as the run is always zero.
Try questions # 5, 8, 6ab, 17, 24a on pages 340-342 in the text.