Question

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

use '<="for < or ">" for >.
(-3,0)
X
5
(0, -3)
-5

Answer 1

Given:

The graph of an inequality.

To find:

The inequality in slope intercept form.

Solution:

The slope intercept form is:

`y=mx+b`

Where, m is slope and b is y-intercept.

From the given graph it is clear that the boundary line passes through the points (-3,0) and (0,-3).

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

`y-0=(-3-0)/(0-(-3))(x-(-3))`

`y=(-3)/(3)(x+3)`

`y=-1(x+3)`

`y=-x-3`

From the given graph it is clear that the boundary line is a solid line and the shaded region lies above the line, so the sign of inequality must be "≥".

`y\geq -x-3`

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