Question

The function f(x) is shown in the graph.

What is the equation for f(x)?



Enter your answer in the box.

F (x) = ?

Answer 1

Answer:
`f(x)=-(3)/(4)x-3`

This is a graph of a Line, the equation of a line is in the following form:

`y=f(x)=mx+b` (1)

Where:

`m` is the slope of the line

`b` is the point of intersection of the line with the y-axis

Now, in order to write the equation (1), we have to find the slope first by the following formula:

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

Where
`(x_(1),y_(1))` and
`(x_(2),y_(2))` are two points of the line.

In this case:

`(x_(1),y_(1))=(-4,0)`

`(x_(2),y_(2))=(0,-3)`

Substituting:

`m=(-3-0)/(0-(-4))` (3)

`m=-(3)/(4)` (4) >>>>This is the slope

Now we have to find the interception with the y-axis, if we look at the graph we will find out the line intercepts with the y-axis in y=-3.

Therefore
`b=-3` (5)

Finally we can write the function:

`f(x)=-(3)/(4)x-3`