Question

Which linear inequality is represented by the graph?

Answer 1

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 $(x_1, y_1)$ and $(x_2,y_2)$ is,

m = $\frac{y_2-y_1}{x_2-x_1}$

For the given points,

m = $\frac{1+3}{3+3}$

m = $\frac{2}{3}$

y-intercept 'b' = -1

Therefore, equation of the given line will be,

$y=\frac{2}{3}x-1$

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 < $\frac{2}{3}x-1$

Therefore, Option (4) will be the answer.