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).

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-0=\dfrac{-3-0}{0-(-3)}(x-(-3))$

$y=\dfrac{-3}{3}(x+3)$

$y=-1(x+3)$

$y=-x-3$

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 $y\geq -x-3$.