SOLUTION: Find the y-intercept. �x � 5y = 15 Graph the inequality. x

SOLUTION: Find the y-intercept. �x � 5y = 15 Graph the inequality. x < �2

Question 112301: Find the y-intercept. �x � 5y = 15
Graph the inequality. x < �2

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Now let's find the y-intercept

To find the y-intercept, let x=0 and solve for y:
Plug in

Simplify

Divide both sides by -5

Reduce

So the y-intercept is

(note: the y-intercept will always have a x-coordinate equal to zero)

In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign).
So lets graph the line (simply draw a vertical line through )
graph of
Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point

Substitute (0,0) into the inequality
Plug in and
Simplify

(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.)

Since this inequality is not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line
Graph of with the boundary (which is the line in red) and the shaded region (in green)
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)

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