Mathematics: Which inequality is represented by this graph !

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Which inequality is represented by this graph

maleyjustinr

11.03.2022

Option A. is the correct option.

Step-by-step explanation:

First we will find the equation of a line passing through two points (0, 1) and (3, 0)

Since equation of a line is represented by y = mx + c

where m = slope of the line

c = y - intercept

For slope $m=\frac{y-y'}{x-x'}$

$m=\frac{1-0}{0-3}=-\frac{1}{3}$

So equation becomes as $y=(-\frac{1}{3})(x)+c$

Since this line passes through (0, 1) so

1 = m(0) + c

c = 1

Now we put the value c = 1 in the equation

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

Since line in the graph is a solid line (not in dotted) and the colored area is below the line, inequality will be "less than equal to".

And the inequality will be $y\leq (-\frac{1}{3})x+1$

Therefore Option A. is the answer.

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