Question

Find the inequality represented by the graph.

Answer 1

Answer:

f(x)<=-1/3x+1

Step-by-step explanation:

so to test this you can do

0<=-1/3(0)+1

0<=1

so it's true

Answer 2

Answer:

y $\leq$ $\frac{-1}{3}x$ + 1

Step-by-step explanation:

To find the inequality represented by the graph, we need to find the linear equation that represents the blue line.

As we can see, the:

y intercept: (0, 1)

x intercept: (3, 0)

So the slope of the equation is:

$m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

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

So use the slope and the slope-point formula, we find the linear expression

The standard form is: y = mx+ b

<=> y = $\frac{-1}{3}$ x + b

Substitute the point (0, 1) to find b, we have:

b= y - $\frac{-1}{3}$ x

<=> b= 1 - 0 =1

So the linear equation is: y = $\frac{-1}{3}$ x + 1

After that, we need to take a test point form the shaded area and evaluate the expression. Let the point be: (1, 2), we have:

2 = $\frac{-1}{3} *1$ +1

<=> 2=$\frac{2}{3}$

We know that 2 > $\frac{-1}{3}$  this means that the left inequality sign is ≥ , so the  inequality represented by the graph:

y $\leq$ $\frac{-1}{3}x$ + 1