2. Write a system of linear inequalities that describes the...

2. Write a system of linear inequalities that describes the shaded region in the graph below. Hint: For each equation, write it in slope-intercept form (if possible) and then based on where the graph was shaded (above or below the line), determine the direction of the inequality symbol. \(2x - 3y = -3\) \(y = 7\) \(x + y = 11\)

Transcript

00:01 Here, we're gonna write a linear inequality whose graph is described by the shaded region.

00:05 And we have two different ones here.

00:07 So the first way i like to start these is by simply finding the equation of the line.

00:14 So if i look at number one here, here's the line, it's right on that edge there, and we're gonna find the equation of that line.

00:21 So i'm gonna start by finding its y -intercept and it's right there at negative two.

00:25 So we're gonna write this equation of the line in y equals mx plus b form, where m is the slope and b is the y -intercept.

00:34 Well, we just said our y -intercept is at negative two.

00:38 So i'm gonna switch that b out and put minus two there.

00:42 And then we need to find the slope.

00:44 So i'm gonna find another slope on the point on the line, and we can see that i go over one and down one.

00:49 So my slope here is negative one because we did have to go negative in one direction.

00:55 So i get negative one x.

00:57 We can actually just write this as negative x minus two.

01:05 It is a solid line, so it does equal that area.

01:10 And if i have this line here, my y values that are shaded are all underneath the line.

01:18 So it's not y equals negative x minus two because that only accounts for this green line that i highlighted here.

01:26 So now we're gonna fix the sign...

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