Question

Write the slope-intercept inequality for the graph below?

Answer 1

Given:

Given that the graph of the inequality.

We need to determine the equation of the inequality.

Slope:

Let us substitute the coordinates (3,-1) and (-3,-3) in the slope formula, we get;

$m=\frac{-3+1}{-3-3}$

$m=\frac{-2}{-6}$

$m=\frac{1}{3}$

Thus, the slope of the inequality is $m=\frac{1}{3}$

Equation of the line:

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

Substituting the point (3,-1) and the slope $m=\frac{1}{3}$, we get;

$y+1=\frac{1}{3}(x-3)$

$y+1=\frac{1}{3}x-1$

     $y=\frac{1}{3}x-2$

Thus, the equation of the line is $y=\frac{1}{3}x-2$

Equation of the inequality:

From the graph, it is obvious that the line of the graph is a dashed line then inequality is either < or >

Thus, the inequality of the equation must be either $y$ or $y>\frac{1}{3}x-2$

Since, the shaded portion of the graph contains the point (0,0), we need to determine the inequality that contains the point.

Hence, substituting (0,0) in the inequality $y$, we get;

$0$

$0$

Thus, the coordinate (0,0) satisfies the condition, then the inequality of the given graph is $y$

Hence, the inequality of the graph is $y$