Answer:
Option 3 is correct. i.e., [tex]y=-\frac{1}{2}x+2[/tex]
Step-by-step explanation:
We are given with a line on proper graph.
So, we find the equation of line by using Two-Point form of line.
Two-Point Form of line states,
if a line passes through 2 point say [tex](x_1,y_1)\:\:and\:\:(x_2,y_2)[/tex], then equation of line is,
[tex](y-y_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
first we find 2 points from graph.
Intersecting points of line with x x-axis and y-axis are (4,0) and (0,2)
so, applying Two-Point form we get
[tex](y-0)=\frac{0-2}{4-0}(x-4)\\\implies y=\frac{-2}{4}(x-4)\\\implies 4.y=(-2).x-4.(-2)\\\implies4y=-2x+8\\\implies y=\frac{-2x}{4}+\frac{8}{4}\\\implies y=-\frac{1}{2}x+2[/tex]
The equation of line is [tex]y=-\frac{1}{2}x+2[/tex]
Therefore, Option 3 is correct.
