Mathematics: This graph shows the solution to which inequality

This graph shows the solution to which inequality

kelsotay623

09.01.2022

The correct option is B.

Step-by-step explanation:

From the given graph it is clear that the related line passing through the points (-3,-3) and (3,-1).

If a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of related line is

$y-(-3)=\frac{-1-(-3)}{3-(-3)}(x-(-3))$

$y+3=\frac{2}{6}(x+3)$

$y+3=\frac{1}{3}(x+3)$

$y+3=\frac{1}{3}(x)+1$

$y=\frac{1}{3}(x)+1-3$

$y=\frac{1}{3}(x)-2$

The equation of related line is $y=\frac{1}{3}(x)-2$ .

Since the related line is dashed and the shaded region is above the line, therefore the sign of inequality is >.

The graph shows the solution to inequality

$y\frac{1}{3}(x)-2$

Therefore the correct option is B.

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