WEBVTT
00:00:01.170 --> 00:00:05.240
A line πΏ passes through points three, three and negative one, zero.
00:00:05.640 --> 00:00:13.310
Work out the equation of the line, giving your answer in the form ππ¦ plus ππ₯ plus π equals zero.
00:00:15.430 --> 00:00:19.400
What weβre going to do first, is work out the equation of the line.
00:00:19.780 --> 00:00:25.630
And after that, weβll focus on moving it into the form ππ¦ plus ππ₯ plus π.
00:00:26.880 --> 00:00:29.040
To solve this problem, weβll need a few things.
00:00:29.530 --> 00:00:32.840
Letβs start with finding the slope and the π¦-intercept.
00:00:34.220 --> 00:00:38.760
The formula for finding slope is, the changes in π¦ over the changes in π₯.
00:00:40.610 --> 00:00:45.560
And we write that, π¦ two minus π¦ one over π₯ two minus π₯ one.
00:00:46.820 --> 00:00:50.640
We plug in these two points for our formula for finding slope.
00:00:51.660 --> 00:00:55.720
π¦ two is zero, minus π¦ one, which is three.
00:00:57.010 --> 00:01:01.020
π₯ two is negative one, minus π₯ one, which is three.
00:01:02.790 --> 00:01:06.390
We end up with negative three over negative four.
00:01:07.600 --> 00:01:11.250
We can simplify our slope to π equals three-fourths.
00:01:12.700 --> 00:01:21.450
Now that we know our π is three-fourths, we can use this slope intercept form to find the intercept of this equation, to find our π.
00:01:22.950 --> 00:01:28.890
So we take our point negative one, zero and we plug those values in for π₯ and π¦.
00:01:30.540 --> 00:01:35.960
This gives us zero equals three-fourths times negative one plus π.
00:01:37.030 --> 00:01:41.450
When I multiply negative one by three-fourths, I get negative three-fourths.
00:01:42.640 --> 00:01:47.550
To get π by itself, I add three-fourths to the right side of the equation.
00:01:47.780 --> 00:01:53.700
And if I add three-fourths to the right side of the equation, I need to add three-fourths to the left side of the equation.
00:01:54.780 --> 00:02:00.480
This means that our π¦-intercept equals three-fourths, π equals three-fourths.
00:02:01.420 --> 00:02:05.660
So we use this formula, and we plug in the π and π that we found.
00:02:07.150 --> 00:02:12.510
This gives us π¦ equals three-fourths π₯ plus three-fourths.
00:02:14.020 --> 00:02:21.840
Now we need to convert the slope intercept form into ππ¦ plus ππ₯ plus π equals zero.
00:02:22.820 --> 00:02:29.950
This means that weβll move everything to the left side of the equation, leaving only zero on the right side of the equation.
00:02:31.230 --> 00:02:35.950
We start that by subtracting three-fourths π₯ from both sides of the equation.
00:02:37.120 --> 00:02:42.000
This leaves us with π¦ minus three-fourths π₯ equals three-fourths.
00:02:43.210 --> 00:02:54.760
Then I can subtract three-fourths from both sides of the equation, which leaves me with π¦ minus three-fourths π₯ minus three-fourths equals zero.
00:02:56.280 --> 00:02:58.110
But this is not our final answer.
00:02:58.490 --> 00:03:10.970
Because when we work with a form like this, we want π, π, and π to be integers, which means we donβt wanna have fractions like three-fourths as π or π.
00:03:12.340 --> 00:03:16.990
To fix this problem, we can multiply our entire form by four.
00:03:18.450 --> 00:03:23.110
We distribute the four to each term in the equation.
00:03:24.550 --> 00:03:26.630
Four times π¦ equals four π¦.
00:03:27.210 --> 00:03:30.720
Four times negative three-fourths equals negative three.
00:03:31.170 --> 00:03:34.280
Four times negative three-fourths equals negative three.
00:03:34.650 --> 00:03:36.440
Four times zero equals zero.
00:03:37.980 --> 00:03:43.700
This is the equation of line πΏ written as ππ¦ plus ππ₯ plus π.
00:03:43.980 --> 00:03:49.090
We would write four π¦ minus three π₯ minus three equals zero.