### Slope-Intercept Form of a Line

#### Lesson Objective

In this lesson, we will examine the slope-intercept form of the equation of a line.

#### About This Lesson

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.

Now, watch the following math video to learn more.

### Math Video

#### Click play to watch video

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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

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