Answered

Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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=

Sagot :

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!

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.