Determine The Equation of a Line
This lesson shows you how to determine the equation of a line using the given information such as the slope, coordinates of a point and more.
About This Lesson
In this lesson, we will learn how to determine the equation of a line using the information given.
This lesson will show you 2 examples on how to do so using the following information:
Point (2,5) and Slope = 2
Points (1,4) and (2,1)
You can proceed by reading the
first or watch the
or try out the
You need to have some knowledge on Slope-Intercept Form of a line. You can learn about it by watching the math video in this
Usually, to determine the equation of a line, we should begin with the Slope-Intercept Form of a line (as shown in the picture).
Next, we just use the information given to find the
However, bare in mind that the information given may not directly help us to find the slope or y-intercept. If this is the case, we need think of way of using the information to find them.
Now, watch the following math video to learn more.
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Math Video Transcript
Determine the Equation of a Line Transcript 00:00:01.120 In this lesson, we will learn how to determine the equation of a line, using the available information. 00:00:08.040 Let's look at the first example. Determine the equation of the line, that passes through the points (2, 5), and with the slope of 2. 00:00:19.000 To begin, we should know that the equation of a line can be written in the form of y = mx + b, where m is the slope, and b is the y-intercept. 00:00:30.110 From this, to determine the equation of the line, we just need to find the values of m and b. 00:00:37.120 Now, we can see that, the slope m, is already given as 2. 00:00:43.050 Therefore, we can just substitute m with 2, and the equation now becomes y = 2x + b. 00:00:51.070 Next, we need to find the y-intercept, b. 00:00:55.090 Since the value of b is not given, we need to find it. 00:00:59.220 To do so, we know that the line passes through the point 2, 5. 00:01:06.160 Therefore, we can use this point by substituting x with 2, and substituting y with 5. 00:01:13.240 With this, notice that we can now solve for b. 00:01:18.010 To solve for b, multiply 2 with 2. This gives 4. 00:01:23.100 Next, add negative 4 to both sides of the equation. This gives 5 - 4 = b. 00:01:30.240 5 minus 4 gives 1. Hence, we found the y-intercept, b as 1. 00:01:38.190 With this, we can write b as 1. 00:01:44.230 Finally, since we found both m and b, the equation of the line is y = 2x + 1 00:01:54.060 Now, next example. 00:01:56.240 Determine, the equation of the line, that passes through the points (1,4) and (2,1). 00:02:04.190 Again, we should know that the equation of a line can be written in the form of y = mx + b. 00:02:12.060 We can see that, the slope and y-intercept are not given. Instead, we only have the coordinates of 2 points. 00:02:20.210 With some thinking, we can use these 2 points to find the slope 'm' by applying the slope formula, (y2-y1)/(x2-x1). 00:02:32.140 To use the slope-formula, we can assign this point as point 1, with the x-coordinate as x1, and y-coordinate as y1. 00:02:42.000 Similarly, we assign the next point as point 2, with x-coordinate as x2, and y-coordinate as y2. 00:02:50.230 Now, we can find 'm' by just substituting, y2 with 1, y1 with 4, x2 with 2, and x1 with 1. 00:03:04.100 Alright, we can remove these brackets, as they do nothing. 00:03:09.220 Let's calculate 'm'. Negative multiply by bracket 4 gives negative 4. negative multiply by bracket 1 gives negative 1. 00:03:20.150 1 minus by 4 give negative 3. 2 minus by 1 gives positive 1. 00:03:27.230 Negative 3 divides by positive 1 gives negative 3. 00:03:32.140 So, we found the slope 'm' as negative 3. Now, we can write m as negative 3. 00:03:42.120 Next, we need to find the y-intercept, b. 00:03:48.080 Now, similar to the previous question, we can find b by taking a point on the line, and substitute its x-coordinate and y-coordinate into the equation. 00:03:59.000 Let's take this point 1,4. 00:04:02.200 Substituting x with 1 and y with 4. 00:04:07.220 Now, we can solve for 'b'. Multiplying negative 3 with 1 gives negative 3. 00:04:14.000 Next, add positive 3 to both sides of the equation. This gives 4 + 3 = b. 00:04:21.120 4 plus 3 gives 7. Hence, we find the y-intercept, b is 7. 00:04:29.010 With this, we can now write b as 7. 00:04:34.120 So finally, with both slope and y-intercept found, we have the equation of the line as, y = negative 3x + 7 00:04:44.060 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 determining an equation of a line
or pick your choice of question below.
on determining the equation of a line using the coordinates of two points.
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