WEBVTT
00:00:03.260 --> 00:00:08.940
Which of the following graphs represents the equation 𝑦 equals negative 𝑥 plus seven?
00:00:11.100 --> 00:00:15.260
So we’ve been given five graphs, each with a different straight line drawn on it.
00:00:15.450 --> 00:00:21.660
And we’re asked to determine which of these represents the straight line whose equation is 𝑦 equals negative 𝑥 plus seven.
00:00:23.520 --> 00:00:28.230
To answer this, let’s consider the slope–intercept form of the equation of a straight line.
00:00:28.550 --> 00:00:35.650
It’s 𝑦 equals 𝑚𝑥 plus 𝑐, where 𝑚 represents the slope of the line and 𝑐 represents the 𝑦-intercept.
00:00:37.240 --> 00:00:44.050
We can compare this general form with the equation that we’ve been given and determine the slope and 𝑦-intercept of our line.
00:00:45.910 --> 00:00:49.980
First of all, we know that the 𝑦-intercept of our line is seven.
00:00:51.680 --> 00:00:57.680
Now let’s look at the five graphs and, specifically, at the point where each of the lines crosses the 𝑦-axis.
00:00:58.160 --> 00:01:03.800
We can see the only lines A and D cross the 𝑦-axis at this point seven.
00:01:04.310 --> 00:01:08.360
The others cross at negative seven, negative one, or negative two.
00:01:10.210 --> 00:01:18.410
For this reason, A and D are currently the only two possibilities remaining for the graph that represents 𝑦 equals negative 𝑥 plus seven.
00:01:19.350 --> 00:01:21.290
Now let’s consider the slope of the line.
00:01:23.160 --> 00:01:28.790
The coefficient of 𝑥 in our equation is negative one, which means the slope of the line is negative one.
00:01:30.270 --> 00:01:38.210
This means that the line slopes downward from left to right and for every one unit you move to the right, the line moves one unit down.
00:01:40.050 --> 00:01:44.400
Looking at lines A and D, we can see that line A slopes upwards.
00:01:44.400 --> 00:01:45.960
It has a positive slope.
00:01:46.300 --> 00:01:48.530
Line D, however, does slope downwards.
00:01:48.530 --> 00:01:50.020
It has a negative slope.
00:01:51.730 --> 00:01:56.790
If we look at line D more closely, we can see that it does indeed have a slope of negative one.
00:01:57.050 --> 00:02:01.260
For every one unit we move to the right, the line moves one unit down.
00:02:03.080 --> 00:02:07.470
Therefore, graph D has both the correct slope and the correct 𝑦-intercept.
00:02:07.630 --> 00:02:12.830
And therefore, graph D represents the equation 𝑦 equals negative 𝑥 plus seven.