### Slope-Intercept Form - Examples

#### Lesson Objective

After learning about the slope-intercept form, let's see some examples on using it to draw the line for any equation of a line (linear equation).

#### About This Lesson

An equation of a line that is in the slope-intercept form can be used to quickly draw the line of that equation.

This lesson will show you how to do so, by using the **slope** and **y-intercept** of any linear equation. We will using the following equations as examples:

- y = -2x +3
- 3y -2x = -6

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 some knowledge on slope-intercept form of a line. You can learn about it by watching the math video in this lesson.

#### Tip #2

If you are given an equation of a line, it **may not** be in the slope-intercept form.

Therefore, it is important to change it into the slope-intercept form (see picture) before we can draw the line. For example, if the equation of the line is given as:

The slope-intercept form for this line will be:

Where **m = 3** and **y-intercept = -2**

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

00:00:01.130

This lesson shows you some examples on how to draw the graph of the equation of a line, that is in the form of slope-intercept.

00:00:09.180

Let's consider the equation, y = -2x + 3.

00:00:15.100

Now, we can see that this equation is already in the slope-intercept form, with the slope as -2, and the y-intercept as +3.

00:00:25.040

So, how do we use the slope and the y-intercept to draw the line?

00:00:30.220

To draw the line, we use the y-intercept first. Since the y-intercept is +3, we know the line will cross the y-axis at +3.

00:00:41.100

Therefore, we can put a point with the coordinates of (0,3) here.

00:00:47.050

Next, with the slope of the line as -2, we can use this information, if we know that the slope is equals to 'change in y' over 'change in x'.

00:00:57.190

Since the 'change in y' over 'change in x' is a fraction, we need to change -2 into a fraction so it can be used.

00:01:06.200

To do so, we simply rewrite -2 as, -2 divides by 1. Since this division gives back -2, the slope remains the same.

00:01:18.190

With this, we now know that the 'change in y' is -2, and the 'change in x' is 1.

00:01:26.130

Now, to use, 'change in y' and 'change in x' , we need to refer these 'change' from a point on the line.

00:01:34.240

Now, the only point that we can refer from, is the point (0,3).

00:01:41.170

So, starting from here, since the 'change in y' is -2, we move down from this point by 2 units.

00:01:50.010

Next, since the 'change in x' is +1, we move from here to the right by 1 unit.

00:01:57.190

Notice that now we have 2 points. By drawing a line through these points, we have the graph of y =-2x + 3.

00:02:07.230

Next example, let's draw the graph of 3y -2x = -6.

00:02:15.000

Now, Notice that we have a problem, this is because the given equation is not in the form of y = m x + b.

00:02:22.120

Hence, we need to manipulate this equation into this form before we can draw it.

00:02:28.000

To do so, we need to make 'y' as the subject of the equation. So, in order to achieve this, we need to remove -2x.

00:02:37.220

We can do so by adding +2x to both sides of the equation.

00:02:42.210

This give 3y = +2x -6. Now, we can remove this positive sign to make the equation looks neater.

00:02:52.200

Next, we need to remove '3' from 3y. To do so, we divide both sides of the equation by 3.

00:03:00.210

By dividing both sides by 3, we get the equation as y = 2x -6 divide by 3.

00:03:08.040

Now, we can split this term into 2 fractions. This gives y = 2x/3 -6/3.

00:03:17.130

6 divides by 3 gives 2.

00:03:20.210

2x divides by 3 can also be written in this way. Finally, you can see that we have change the equation into the form of y = mx + b.

00:03:32.100

Now, clearly the y-intercept is -2. Hence, the line will cross the y-axis at -2.

00:03:40.050

Therefore, we can put a point with the coordinates of (0,-2) here.

00:03:45.180

Next, we know that 2/3 is the slope with the 'change in y' of 2 and the 'change in x' of 3.

00:03:55.040

Now, to use, 'change in y' and 'change in x', we need to refer these 'change' from a point on the line.

00:04:03.220

The only point that we can refer from, is the point (0, -2)

00:04:09.140

So, starting from here, since the 'change in y' is +2, we move up from this point by 2 units.

00:04:17.200

Next, since the 'change in x' is +3, we move from here to the right by 3 units.

00:04:25.130

Notice that now we have 2 points. By drawing a line through these points, we have the graph of 3y -2x = -6.

00:04:36.200

That is all for this lesson. Try out the practice question to further your understanding.

### 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 or pick your choice of question below.

- Question 1 on the changing an equation of a line into slope-intercept form
- Question 2 on drawing a line by referring to the slope and y-intercept of a line

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