Answer:
Option (d) is correct.
[tex]3y+x>6[/tex] and [tex]y>2x+4[/tex]
Step-by-step explanation:
Given : A graph
We have to choose the system of linear inequalities is represented by the graph .
Let take two points on each line
We have (0,2) and (6,0) on one line
Then equation of line is of the form y = mx + b , where, m is slope and b is y- intercept.
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(6,\:0\right)[/tex]
[tex]m=\frac{0-2}{6-0}=\frac{-1}{3}[/tex]
Thus, Equation of line is [tex]y=\frac{-1}{3}x+2[/tex]
Simplify, we have,
[tex]3y+x=6[/tex]
Since, (3,2) is the point in the region so substitute, we get,
[tex]3(2)+3>6[/tex]
Therefore, Inequality becomes, [tex]3y+x>6[/tex]
Similarly, for second line
We have (0,4) and (-2,0) on one line
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{0-4}{-2-0}=2[/tex]
Thus, Equation of line is [tex]y=2x+4[/tex]
Since, (-3,1) is the point in the region so substitute, we get,
[tex]1>-6+4=-2[/tex]
Therefore, Inequality becomes, [tex]y>2x+4[/tex]
Thus, Inequality becomes
[tex]3y+x>6[/tex] and [tex]y>2x+4[/tex]
