Slope-Intercept Form of a Line

Lesson Objective

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 study tips first or watch the math video or try out the practice questions.

Study Tips

Tip #1

This lesson involve both slope the and y-intercept. If you need to recall them, you can watch the math videos in:

Tip #2

An equation of a line can be written in many forms. Some of these forms are listed below:

Slope-Intercept Form
Point-Slope Form
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.

Math Video

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If the above player doesn't work, try this direct link.

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.

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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.

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Now, the line for this equation, y = 2x+3 is shown on the graph.

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 Since the y-intercept is +3, naturally, this line will cross the y axis at 3. 

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Alright, when I decrease the y-intercept, notice how the line changes accordingly. 

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When the y-intercept is changed to +2, note that the line will cross the y-axis at +2.

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We will observe a similar behavior when the y-intercept is changed to positive 1, zero, -1,  -2, and so on.

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Also, notice that, since we are only changing the y-intercept, the slope of the line remains the same.

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Next, let's examine the slope, m.  When I change the slope, notice how the steepness of the line changes.

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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?

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To know this, let us decrease the slope. 

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Now, see that when the slope is zero, the line becomes parallel to the x-axis.

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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.

Question 1 on the basics of slope-intercept form

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