Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

Represent to Solution Set of Each of the Following Inequations Graphically in Two Dimensional Plane: Y ≥ 2x − 8 - Mathematics

Represent to solution set of each of the following inequations graphically in two dimensional plane:

y ≥ 2x − 8

Solution

Converting the inequation to equation, we obtain 2x $-$ y$-$8 =0
Putting y = 0 and x = 0 in this equation, we obtain x = 4 and y = $-$8 respectively.
So, this line meets the x-axis at (4,0) and y-axis at (0,$-$8).
We plot these points and join them by a thick line.This divides the xy plane into two parts.
To determine the region represented by the given inequality, consider point O(0,0).
Clearly, (0,0) does satisfy the inequality.
So, the region containing the origin is represented by the given inequality.
Hence, the shaded region is the solution to the inequation.

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Exercise 15.5 | Q 9 | Page 28