Question

Which linear inequality is represented by the graph?1. y≤ 2x+42. y≤ x+33. y²x+34. y≥ 2x+3

Answer 1

Given a graph represented a linear inequality.

First, we will find the equation of the shown line.

As shown, the line passes through the points (0, 3) and (2, 4)

the general equation of the line in the slope-intercept form will be:

`y=mx+b`

Where (m) is the slope and (b) is the y-intercept

b = y-intercept = 3

We will find the slope as follows:

`m=(y_2-y_1)/(x_2-x_1)=(4-3)/(2-0)=(1)/(2)`

So, the equation of the line will be:

`y=(1)/(2)x+3`

As shown, the point (0, 0) lying in the area of the solution

So, the linear inequality will be as follows:

`y\leq(1)/(2)x+3`