Question

4. What is the system of equations that describes the following graph?

Answer 1

Answer:

The system of inequalities is

$y$

$y>0.25x$

Step-by-step explanation:

step 1

Find the equation of the dashed line with negative slope

The line passes through the points

(0,-2) and (-2,0)

Find the slope

$m=(0+2)/(-2-0)=-1$

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=-1\\b=-2$

substitute

$y=-x-2$

The solution of the inequality is the shaded area below the dashed line

therefore

The equation of the inequality A is

$y$

step 2

Find the equation of the dashed line with positive slope

The line passes through the points

(0,0) and (4,1)

Find the slope

$m=(1-0)/(4-0)=0.25$

Find the equation of the line (direct variation)

$y=kx$

we have

$k=0.25$

substitute

$y=0.25x$

The solution of the inequality is the shaded area above the dashed line

therefore

The equation of the inequality B is

$y>0.25x$

therefore

The system of inequalities is

$y$

$y>0.25x$