Question

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

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:

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

$y-(-2)=\dfrac{1-(-2)}{1-0}(x-0)$

$y+2=\dfrac{1+2}{1}(x)$

$y+2=3x$

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 $y\geq 3x-2$.