Question

What system of linear inequalities is shown on the graph?

Answer 1

Top is the dotted , bottom is the solid

Answer 2

Answer:

$3y-x$

$2x+y\leq2$

Step-by-step explanation:

Equation of line that passes two points (a,b) and (c,d) :

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

Dotted line passes through (0,2) and (-3,1).

Equation of Dotted line :

$(y-2)=\dfrac{1-2}{-3-0}(x-0)$

$(y-2)=\dfrac{-1}{-3}x$

$3(y-2)=x$

$3y-6=x$

$3y-x=6$

Inequality for dotted line (values on line is not included for dotted)

$3y-x$  (shaded below )

Solid line passes through (0,2) and (1,0)

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

$y-2=-2x$

$2x+y=2$

Inequality for dotted line (values on line is included for solid line)

$2x+y\leq2$ (shaded leftwards )

∴ System of linear inequalities is shown on the graph:

$3y-x$

$2x+y\leq2$