Year 10+ Coordinate Geometry
Chapters
Slope of a Straight Line
Slope of a Straight Line
The slope of a straight line is a number that tells you how steep it is. Another word for slope is gradient.
Finding the Slope
-of-a-straight-line/gradientdef1.png)
The slope is given by the following formula:
Vertical Rise Over Horizontal Run
-of-a-straight-line/gradientdef2.png)
We often call the change in height the vertical rise, and the change in horizontal distance the horizontal run, so the formula for the slope can be written as :
Let's calculate the slopes of some lines.
Example 1
-of-a-straight-line/example1.png)
The vertical rise is \(2\) and the horizontal run is \(4\), so the slope is
Example 2
-of-a-straight-line/example2.png)
The vertical rise is \(4\) and the horizontal run is \(4\), so the slope is
Did you notice that this line is steeper than the line in Example 1? Its slope is larger, too.
Example 3
-of-a-straight-line/example3.png)
The vertical rise is \(5\) and the horizontal run is \(2\), so the slope is
This line is even steeper than the line in Example 2. Its slope is larger, too.
Sign of the Slope
Slopes can be positive, negative or zero.
-
When the slope is
positive, the straight line is going uphill as we move from left to right. We say that the straight line function isincreasing. -
When the slope is
negative, the straight line is going downhill as we move from left to right. We say that the straight line function isdecreasing. - When the slope is
zero, the straight line is horizontal. It slopes neither uphill nor downhill.
-of-a-straight-line/increasinganddecreasingslope.png)
Example: Negative Slope
-of-a-straight-line/example5.png)
The vertical rise is \(-3\) as the line is sloping downwards, and the horizontal run is \(2\), so the slope is
This line is sloping downhill, so it has a negative slope.
Example: Zero Slope
-of-a-straight-line/example4.png)
The vertical rise is \(0\) as the line is horizontal (flat), and the horizontal run is \(4\), so the slope is
This line is horizontal, so its slope is zero.
Example: Vertical Line
The vertical rise is \(4\), and the horizontal run is \(0\) as the line is vertical, so the slope is
That's a bit of a problem, isn't it? We say that the slope of vertical lines is undefined.
Summary
The slope of a line that slopes uphill is positive.
The slope of a line that slopes downhill is negative.
The slope of a horizontal line is zero.
The slope of a vertical line is undefined.
Steeper (uphill) lines have larger slopes.
Steeper downhill lines have negative slopes that have larger sizes.
Description
A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates. In this tutorial series, you will learn about vast range of topics such as Cartesian Coordinates, Midpoint of a Line Segment etc
Audience
year 10 or higher, several chapters suitable for Year 8+ students.
Learning Objectives
Explore topics related to Coordinates Geometry
Author: Subject Coach
Added on: 27th Sep 2018
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