Answered

Which inequality is represented by the graph
(Pic attached) Options: A. y> - 2/3 x + 1 ,
B. y< -2/3 x + 1 , C. y< -3/2 x + 1, D. y> -3/2 x + 1​

Which inequality is represented by the graph Pic attached Options A ygt 23 x 1 B ylt 23 x 1 C ylt 32 x 1 D ygt 32 x 1 class=


Answer :

Answer:

C. y< -3/2 x + 1

Step-by-step explanation:

Solving the Problem

Finding the Equation of the Line

Using the slope formula we can find the m value of the line's equation

(y = mx + b).

Using the points (-2,4) and (2,-2),

             [tex]slope=\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{4-(-2)}{-2-2}=\dfrac{6}{-4} =-\dfrac{3}{2}[/tex].

So, [tex]y=-\dfrac{3}{2}x+b[/tex].

To find the y-intercept of the line we just look at where the line intercepts the y-axis.

It intersects at 1, so b = 1!

Our line's equation is [tex]y=-\dfrac{3}{2}x+1[/tex].

This eliminates choices A and B.

[tex]\dotfill[/tex]

Determining the Inequality Sign

Inequalities can have several correct answers to satisfy the expression.

If we plug in one of the points in the shaded region into either C or D, one of them should evaluate to true and thus indicate our final answer!

Let's choose the origin (0,0) as our testing point.

Plugging into C:

                                       [tex]0 < -\dfrac{3}{2} (0)+1[/tex]

                                                [tex]0 < 1[/tex],

this is true.

Plugging into D:

                                        [tex]0 > \dfrac{3}{2}(0)+1[/tex]

                                             [tex]0 > 1[/tex],

this is false.

So, C is our final answer!