Question

What is the linear function equation represented by the graph?


f (x) = ?

Answer 1

`f(x)=-(1)/(2)x+2`

Explanation:

We have been given a graph of a function and we are asked to find the equation for our given function.

We will write formula for our given function in slope-intercept form of equation:
`y=mx+b`, where,

m = Slope of line,

b = The y-intercept or initial value.

Let us find slope of our given line using slope formula.

`m=(y_2-y_1)/(x_2-x_1)`, where,

`y_2-y_1` = Difference between two y-coordinates,

`x_2-x_1` = Difference between two x-coordinates of same y-coordinates.

Upon substituting coordinates of points (0,1) and (2,0) in slope formula we will get,

`m=(0-1)/(2-0)`

`m=(-1)/(2)`

`m=-(1)/(2)`

We can see that initial value of our function is 2, so y-intercept will be 2.

Upon substituting our given values in slope-intercept form of equation we will get our function formula as:

`f(x)=-(1)/(2)x+2`

Therefore, the equation
`f(x)=-(1)/(2)x+2` is represented by our given function.