This lesson shows you how the slope formula is derived and some visual examples on using it.
About This Lesson
After defining the slope of a line as the ratio of the 'change in y' and 'change in x', we can use this definition to derive the slope formula.
This lesson will show you logical steps in deriving this formula. Also, you will able to see some visual examples on using this formula.
You can proceed by reading the
first or watch the
or try out the
Understand how the 'change in y' and 'change in x' are calculated. To recall them, you can watch the math video in the
slope of a line lesson
It is important to
the slope formula before using it. You will be more comfortable using the formula once you have understood it.
Now, watch the following math video to learn more.
Click play to watch video
Your browser does not support Flash or HTML5 video. You can:
upgrade your browser
try this direct link
If the above player doesn't work,
try this direct link
Math Video Transcript
00:00:01.110 In this lesson, we will learn how to derive and use the slope formula. 00:00:06.190 From the previous lesson, we learn that the slope of a line is equals to, 'change in y' divides by 'change in x'. 00:00:14.160 Using this definition, we can now derive the slope formula. 00:00:19.210 Let's put the first point on the coordinate plane. 00:00:23.150 Now,since we are deriving a formula, we can represent the x-coordinate and y-coordinate as x1, and y1 respectively. 00:00:33.070 Let's put the second point on the plane. 00:00:37.130 Again, we can represent the x-coordinate and y-coordinate as x2, and y2 respectively. 00:00:44.110 Now, with these two points, we can draw a straight line and derive the slope formula from here. 00:00:51.230 Now, imagine that we run from, x1 to x2. The change in x would be x2 minus x1. 00:01:02.050 Alright, with this, we can replace 'change in x' with 'x2 minus x1'. 00:01:08.220 Next, referring to the y-coordinates, when we climb up from here, the "change in y" will be, y2 minus y1. 00:01:19.070 Now, with this, we can replace 'change in y' with 'y2 minus y1'. 00:01:26.120 Finally, the slope is equals to, "y2 minus y1" divides by "x2 minus x1". 00:01:34.130 Following the convention, we can represent the slope with the variable m. 00:01:40.190 So, we now have the slope formula, m equals to, "y2 minus y1" divides by "x2 minus x1". 00:01:49.240 Alright, let's use this formula to find the slope of this line. 00:01:55.190 Let's view the actual coordinates for the first point. we have, x1 as 2.0, and y1 as 3.0. 00:02:05.060 Similarly, for the second point, we have x2 as 5.0, and y2 as 6.0. 00:02:13.180 Now, we can find the slope of this line by simply substituting these coordinates into the slope formula. 00:02:20.180 Let me show you, substituting y2 with 6, y1 with 3, x2 with 5, and x1 with 2. 00:02:36.010 Now, we can see that we do not need these brackets. So, let's remove them. 00:02:42.020 Let's simplify this, negative multiply by bracket 3.0 gives negative 3.0. 00:02:49.060 Negative multiply by bracket 2.0 gives negative 2.0. 00:02:54.160 6.0 minus 3.0 gives positive 3.0. 5.0 minus 2.0 gives positive 3.0. 00:03:04.120 Now, positive 3 divides by positive 3 gives positive 1. 00:03:09.220 So, the slope of this line is positive 1. 00:03:15.100 Let's take a look at another example. But first, let me change the coordinates of these points. 00:03:24.100 Using this formula, we can substitute y2 with 4.0, y1 with negative 1.0, x2 with 1.0, and x1 with 6.0. 00:03:40.130 Now, we can see that we do not need these brackets. So, let's remove them. 00:03:46.170 Let's simplify this, negative multiply by bracket negative 1.0 gives positive 1.0 00:03:54.080 Negative multiply by bracket 6.0 gives negative 6.0. 00:03:59.240 4.0 plus 1.0 gives positive 5. 1.0 minus 6.0 gives negative 5. 00:04:09.130 Now, positive 5.0 divides by negative 5.0 gives negative 1. 00:04:17.050 So, the slope of this line is negative 1. 00:04:21.200 That's all for this lesson, try out the practice question to test your understanding.
Multiple Choice Questions (MCQ)
Now, let's try some MCQ questions to understand this lesson better.
You can start by going through the series of
questions on slope formula
or pick your choice of question below.
on using the slope formula
Return to Home Page
. All Rights Reserved.
This is an offline version of MathExpression.com for the WorldPossible.org's RACHEL project. Enjoy!