# Math Help - graph

1. ## graph

FIRST PROBLEM
The equation:

|x/2| + |y/2| = 5

encloses a certain region on a coordinate plane. What is the area of this region?

SECOND PROBLEM
How many different numbers are there such that ax + b = c (a,b,and c are constants) ?
1. c>b
2. a>1

A. Statement 1. is sufficient
B. Statement 2. is sufficient
C. Statements 1. and 2. together are sufficient
D. Each statement alone is sufficient
E. Both statements together are not sufficient

thank you

2. Originally Posted by simone

FIRST PROBLEM
The equation:

|x/2| + |y/2| = 5

encloses a certain region on a coordinate plane. What is the area of this region?

...
Hi,

use the property of an absolute value:

$| x | = \left\{\begin{array}{lr}x , & \text{ if } \geq 0 \\ -x , & \text{ if } < 0 \end{array} \right.$

You get 4 different equations:
$
\left|\frac y2\right|+\left|\frac x2 \right| = 5 ~\iff~\left\{\begin{array}{lr}y \geq0 \wedge x\geq 0\rightarrow & y = -x+10 \\y \geq 0 \wedge x < 0 \rightarrow & y = x+10 \\y < 0 \wedge x\geq 0 \rightarrow & y = x-10 \\ y < 0 \wedge x < 0 \rightarrow & y = -x-10\end{array}\right.$

These 4 lines form a square: see attachment.

If these lines are supposed to enclose a region as stated in the text of your problem then you have to replace the = sign by a $\leq$ sign.