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

B.) y > 3x + 2

Explanation:

Answer 2

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

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=(y_2-y_1)/(x_2-x_1)`

`m=(-7-2)/(-3-0)`

`m=(-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`