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3 years ago

HOW TO GRAPH x + 2y ≥ -6

Mathematics

1 answer:

Zolol [24]3 years ago

8 0

Answer: The graph is attached (See explanation).

Step-by-step explanation:

The Slope-Intercept form of the equation of the line is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given inequality:

$x + 2y \geq -6$

You need to solve for "y":

$2y \geq -x-6\\\\y\geq -\frac{1}{2}x-3$

You can identify that the line is:

$y= -\frac{1}{2}x-3$

Which slope and y-intercept are:

$m=-\frac{1}{2}\\\\b=-3$

To find the x-intercept, substitute $y=0$ into the equation and solve for "x":

$0= -\frac{1}{2}x-3\\\\3= -\frac{1}{2}x\\\\(3)(-2)=x\\\\x=-6$

Then, you know that the line passes through the points (0,-3) and (-6,0), so you can graph it.

The symbol $\geq$ indicates that the line is solid and you must shade the region above the line.

So, you get the graph attached.

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