Question

Graph the solution sets of the following inequations: 

y - 2 ≤ 3x

Answer 1

Given y - 2≤3x 

⇒ y≤3x + 2 

Consider the equation y = 3x + 2 

Finding points on the coordinate axes: 

If x = 0, the y value is 2 i.e., y = 2 

⇒ the point on Y axis is A(0,2) 

If y = 0, 0 = 3x + 2 

⇒x = \(-\frac{3}{2}\)

The point on the X axis is B( \(-\frac{3}{2}\) ,0) 

Plotting the points on the graph: fig. 

Now consider the inequality y ≤ 3x + 2 

Here we need the y value less than or equal to 3x + 2 

⇒ the required region is below point A. 

Therefore the graph of the inequation y ≤ 3x + 2 is fig. 

figure