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!
