Question

Which equation is represented by the graph below?

Answer 1

the answer is y = -1/2x+2.

Answer 2

Option 3 is correct. i.e.,
`y=-(1)/(2)x+2`

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
`(x_1,y_1)\:\:and\:\:(x_2,y_2)`, then equation of line is,

`(y-y_1)=(y_2-y_1)/(x_2-x_1)(x-x_1)`

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

`(y-0)=(0-2)/(4-0)(x-4)\\\implies y=(-2)/(4)(x-4)\\\implies 4.y=(-2).x-4.(-2)\\\implies4y=-2x+8\\\implies y=(-2x)/(4)+(8)/(4)\\\implies y=-(1)/(2)x+2`

The equation of line is
`y=-(1)/(2)x+2`

Therefore, Option 3 is correct.