Question

Y"
2. Sketch the graph of each of following inequations in
XOY-coordinate system :
(i) x > 5y
​

Answer 1

Working rule :

★ Write the equation corresponding to the given inequation .

Here ,

The given inequation is : x > 5y

The corresponding equation will be ;

x = 5y

★ Choose two or three points to draw the graph of corresponding equation .

• If y = 0 , then x = 5•0 = 0 .

Thus , Point is (0 , 0)

• If y = 1 , then x = 5•1 = 5 .

Thus , Point is (5 , 1)

★ Mark those points on the graph paper and join them with scale .

→ If the inequation contains the inequality < or > , then join the points with broken line .

→ If the inequation contains the inequality ≤ or ≥ , then join the points with continuous line .

Here ,

The inequation contains > , thus join the points with broken line .

★ Clearly , the drawn line will divide the XOY plane in two regions . Choose a point on either the sides of drawn line (corresponding equation) .

Here ,

Let's choose the point (5 , -5) .

★ Put the coordinates of the chosen point in the given inequation .

→ If the inequation is true for that particular point , then shade the region containing that point .

→ If the inequation is false for that particular point , then shad the other region not containing that point .

Here ,

The chosen point is (5 , -5) .

Now ,

Putting x = 5 and y = -5 in the given inequation , we get ;

=> x > 5y

=> 5 > 5•(-5)

=> 5 > -25 (which is a true statement)

Thus ,

Shade the region containing the point

(5 , -5) .

Hence ,

The graph of the given inequation is obtained .

(For graph , please refer to the attachment)