Slope-Intercept Form Examples
Lesson Objective
After learning about the
slope-intercept form
, let's see some examples on how to use it to draw the line of a linear equation.
About This Lesson
The Slope-Intercept From of a line equation contains valuable information that can be used to quickly draw the line of the linear equation.
This lesson will show you on how to draw the line using
slope
and
y-intercept
of a line of the following equations:
y = -2x +3
3y -2x = -6
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 some knowledge on Slope-Intercept Form of an equation of a line. You can recall it by watching the math video in this
lesson
.
Tip #2
An equation of a line given
may not
be in the Slope-Intercept Form.
Therefore, it is important to change it to Slope-Intercept Form (see picture) before we can draw the line.
For example, if the given equation of the line is:
2y - 6x = -4
The Slope-Intercept form for this line is:
y = 3x -2
Where
m = 3
and
y-intercept = -2
Now, watch the following math video to learn more.
Math 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
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