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).

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:

                   2y - 6x = -4

The slope-intercept form for this line will be:

                    y = 3x -2

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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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

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.

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