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.