Answer:
Option (4)
Step-by-step explanation:
From the graph attached,
A dotted line passes through two points (3, 1) and (-3, -3)
Let the equation of the given line is,
y = mx + b
where 'm' = slope of the line
b = y-intercept
Slope of a line passing through [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
For the given points,
m = [tex]\frac{1+3}{3+3}[/tex]
m = [tex]\frac{2}{3}[/tex]
y-intercept 'b' = -1
Therefore, equation of the given line will be,
[tex]y=\frac{2}{3}x-1[/tex]
Since graphed line is a dotted line so it's representing an inequality(having < or > sign)
And the shaded part is below the dotted line,
Inequality will be,
y < [tex]\frac{2}{3}x-1[/tex]
Therefore, Option (4) will be the answer.
