Question

Write an inequality, in slope-intercept form, for the graph below. If necessary,

use "<=" for < or ">" for >.

Can anyone pls help ?

Answer 1

Given:

The graph of a linear inequality.

The boundary line passes through the points (0,-2) and (1,1), and the shaded region lies above the boundary line.

To find:

The inequality for the given graph.

Solution:

The boundary line passes through the points (0,-2) and (1,1), so the equation of the boundary line is:

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

`y-(-2)=(1-(-2))/(1-0)(x-0)`

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

`y+2=3x`

Subtract 2 from both sides.

`y=3x-2`

The boundary line is a solid line and the shaded area lies above the boundary line, so the sign of inequality must be
`\geq`.

`y\geq 3x-2`

Therefore, the required inequality is
`y\geq 3x-2`.