# Graphing inequalities

• Jan 24th 2007, 09:36 PM
mike1
Graphing inequalities
I have to choose a system of inequalities that corresponds to a graph I have. My graph is of a circle with the center being (0,0) in the center. A line is drawn from the (-[sqrt]5, [sqrt]5) the 315 deg. position to the ([sqrt]5, -[sqrt]5) the 135 deg. position. Everything from 315 deg. to 360 deg. and from 000 deg. to 135 deg. is shaded in. I'm not sure how to draw it on this page or I would.

a. {x<y
{x[squared]+y[squared]<10

b. {x>y
{x[squared]+y[squared]<10

c. {x-y>0
{x[squared]+y[squared]<10

d. {x+y>0
{x[squared]+y[squared]<10
• Jan 24th 2007, 09:57 PM
earboth
Quote:

Originally Posted by mike1
I have to choose a system of inequalities that corresponds to a graph I have. My graph is of a circle with the center being (0,0) in the center. A line is drawn from the (-[sqrt]5, [sqrt]5) the 315 deg. position to the ([sqrt]5, -[sqrt]5) the 135 deg. position. Everything from 315 deg. to 360 deg. and from 000 deg. to 135 deg. is shaded in. I'm not sure how to draw it on this page or I would.

a. {x<y
{x[squared]+y[squared]<10

b. {x>y
{x[squared]+y[squared]<10

c. {x-y>0
{x[squared]+y[squared]<10

d. {x+y>0
{x[squared]+y[squared]<10

Hello,

I've attached a diagram to show you what I've done:

According to your problem the circle has the equation:

$x^2+y^2=10$

The coordinates of all points which lay inside the circle satisfy the inequality

$x^2+y^2 \leq 10$

The given straight line has the equation y = -x. You are looking for points situated above this line. Therefore y ≥ -x.

Therefore answer d. is correct if the 2 statements are connected by a logical and, that means $\wedge$.

EB