00:01
In this question we have a graph that represents a system of linear inequalities.
00:07
So what we want to do is to determine the system of linear inequalities that best describes the graph.
00:15
So the first thing we need to do is to get the boundary lines.
00:18
So there are several lines.
00:20
There's one line passing here.
00:23
There's a rising line.
00:24
That's a fast line.
00:26
And there's a falling line here.
00:30
So we want to get the equations of those two lines.
00:36
To get the equations we need to get the slope and the y intercept.
00:44
Now let's start with this, the rising line.
00:47
The rising line will have the form y equals mx plus c and we notice that the y intercept is negative 2 so that's going to be y equals mx, mx, much, and we notice that the y intercept is negative 2.
01:02
Minus 2 and the slope of the line is given by the rise over the run so the rise is 2 and the run is 2 so the slope is 2 over 2 which makes it 1 so let's just change this to 1x or the equation of the line is simply y equals x minus 2 so that's the boundary line here y equals x minus 2 the part that has been shaded is the part is the region where y is greater than x minus 2 and so we are not interested in that region our interest is the on the unshaded part to see the unshaded part is the region where y is less than x minus 2 the next thing you need to look at is the line is it a solid line or a dotted line it's a solid line and therefore we have to put y is less than or equal to, y is less than or equal to negative 2.
02:14
And for the top part, it's going to be y is greater than or equal to negative 2.
02:20
Next we have the second line.
02:24
The second line has a y intercept of 2 and it's a falling line.
02:30
So the equation of the line is y equals mx plus 2.
02:35
Now let's get the rise over the run...