Question

Which linear inequality is represented by the graph?

Answer 1

Answer:

$y ≤ \frac{1}{3}x - 1.3$

Step-by-step explanation:

The graph of the inequality is shown here and we have to select the right equation of the graphed inequality.

Now, the zone of solution includes the straight line which passes through the points (3,-0.3) and (0,-1.3)

This points satisfies the equation $y = \frac{1}{3}x - 1.3$ .......... (1)

Therefore, the equation of the inequality will be either $y ≤ \frac{1}{3}x - 1.3$ or $y ≥ \frac{1}{3}x - 1.3$.

Now, choose any one point in the graphed solution zone. Say the point is (2,-2).

Now, from equation (1) we get the right hand side putting x = 2, we get  

$\frac{1}{3} \times 2 - 1.3 = -0.633$. So, -2 is less than -0.633.

Therefore, the correct equation of the inequality is $y ≤ \frac{1}{3}x - 1.3$ (Answer)