Question

Enter the correct answer in the box. Write your answer in the form y - mx + b, using the appropriate inequality symbol in place of
the equal sign.
What inequality is shown in the graph?

Answer 1

Hello and Welcome to Brainly!

Let's take this problem step-by-step:

The problem wants the final answer to be in the form ⇒ y = mx + b

• m ⇒ value of the slope
• b ⇒ y-intercept

Let's find both of these values first

• $slope = \frac{y_2-y_1}{x_2-x_1}$

            (x₁,y₁), (x₂,y₂) are any two points on the line

                 ⇒ let's use (-4,0) and (0,-4)

                      $Slope = \frac{-4-0}{0--4} =\frac{-4}{4} =-1$

• the y-intercept is any coordinate whose x-coordinate equals '0'

           ⇒, therefore, the y-intercept is -4

Our equation as of now: y __ -x - 4

Now let's use some points to test:

  ⇒ what way inequality should face:

• test with (0,0) (within the shaded region)

       $0 _._._. -(0) - 4\\0 _._._. -4\\0 \geq -4$

Therefore our equation is $y\geq -x-4$

  * we use '≤' since the line is solid

        ⇒ if the line were dotted, we would use '>'

Answer: y ≥ -x - 4

Hope that helps!

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