Question

Which linear inequality is represented by the graph? y < 3x + 2 y > 3x + 2 y < 1/3x + 2 y > 1/3x + 2

Answer 1

Answer:

$y>3x+2$ is represented in the graph.

Step-by-step explanation:

To find the linear inequality for the shown graph.

Steps:

Finding the equation of dotted line shown in the graph.

Equation of line is given by

$y=mx+b$

where $m$ is slope of line and $b$ is y-intercept.

Given points: $(0,2) \ and\ (-3,-7)$

Slope of the line $m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-7-2}{-3-0}$

$m=\frac{-9}{-3}$

∴ $m=3$

From the given points we can see that point of y-intercept is given i.e. the point where the line intersects the y-axis  $(0,2)$

∴ $b=2$

So equation of line:

$y=3x+2$

Since the shaded area in the graph is above the line and the line is dotted this means that $y$ is greater than the equation of line.

So, the inequality can be given as:

$y>3x+2$