Slope-Intercept Form of a Line
In this lesson, we will examine the slope-intercept form of an equation of a line.
About This Lesson
After learning about the slope and the x- & y-intercept of a line, it is time to learn about the equation of a line that contains both the slope and y-intercept (Slope-Intercept Form).
This lesson will show how will the graph of the line will change for different values of slope and y-intercept.
You can proceed by reading the
first or watch the
or try out the
This lesson involve both slope the and y-intercept. If you need to recall them, you can watch the math videos in:
Slope of a Line
x-intercept and y-intercept
An equation of a line can be written in many forms. Some of these forms are listed below:
Two Point Form
An equation of a line can be manipulated and changed into any of these forms.
Now, watch the following math video to learn more.
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Math Video Transcript
00:00:01.190 In this lesson, we will examine the slope-intercept form of an equation of a line. 00:00:07.080 The equation of a straight line can be written in the form of y =, m x + b, where m is the slope, and b is the y-intercept. 00:00:16.220 As for y and x, they are just variables, and can be represented in the graph as y-axis and x-axis respectively. 00:00:25.100 As you can guess, this equation of a line is in the Slope-Intercept form because it contains both the slope and y-intercept. 00:00:32.190 Now, to understand more about y = m x + b, let's take a look at this line: y = 2x + 3. 00:00:42.200 By comparing y = 2x +3 with y = m x +b, we can see that the slope of the line is 2, and the y-intercept is +3. 00:00:53.170 Now, the line for this equation, y = 2x+3 is shown on the graph. 00:01:00.200 Since the y-intercept is +3, naturally, this line will cross the y axis at 3. 00:01:08.160 Alright, when I decrease the y-intercept, notice how the line changes accordingly. 00:01:14.220 When the y-intercept is changed to +2, note that the line will cross the y-axis at +2. 00:01:22.130 We will observe a similar behavior when the y-intercept is changed to positive 1, zero, -1, -2, and so on. 00:01:34.090 Also, notice that, since we are only changing the y-intercept, the slope of the line remains the same. 00:01:47.100 Next, let's examine the slope, m. When I change the slope, notice how the steepness of the line changes. 00:01:55.200 As I increases the slope from +2 to +3, we can see that the line becomes steeper. 00:02:03.160 So, you can see that, the line becomes steeper as the slope continues to increase. 00:02:09.240 Also, note that, when the slope is positive, the line slants upward to the right. 00:02:16.170 Next, since we only change the slope, the y-intercept remains same and the line will naturally crosses the y-axis at +1. 00:02:26.080 Alright, what happens to the line when the slope, m, is zero or negative? 00:02:33.020 To know this, let us decrease the slope. 00:02:35.240 Now, see that when the slope is zero, the line becomes parallel to the x-axis. 00:02:43.170 As the slope becomes negative, the line now slants upward towards the left, and the steepness of the line increases as the slope becomes more negative. 00:02:54.020 That is all we need to know about y = mx + b for now, we will learn more about in the next lesson.
Practice Questions & More
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-Intercept Form
or pick your choice of question below.
on the basics of slope-intercept form
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