### Slope-Intercept Form of a Line #### Lesson Objective

In this lesson, we will examine the slope-intercept form of the equation of a line. After learning about the slope, x-intercept and y-intercept of a line, it is time for you to learn about the equation of a line that has both the slope and y-intercept (slope-intercept form of a line).

This lesson will show you how the graph of the line will change for different values of slope and y-intercept.

You should proceed by reading the study tips and watch the math video below. After that, you can try out the practice questions. ### Study Tips #### Tip #1

This lesson involves the slope 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 changed into any of these forms.

### Math Video #### Click play to watch video You can contribute to the development of this site and keep it free by getting all six video lessons and volume of solids and calculator app for just US\$1.99 from Apple App Store.

I'd like to contribute or to know more about the app #### 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.

• Question 1 on the basics of slope-intercept form #### Site-Search and Q&A Library

Please feel free to visit the Q&A Library. You can read the Q&As listed in any of the available categories such as Algebra, Graphs, Exponents and more. Also, you can submit math question, share or give comments there. 