Question

Write a rule to describe the function shown.

Answer 1

`y=(2)/(3) x`

Explanation:

Assuming a straight line function, the following formula can be used:

`y=mx +c\\`

Where c is the y intercept, and m is the slope of the function. The y intercept of a function is the value where x = 0, which in this case is zero, giving the function:

`y=mx`

Find the slope using the first two points:

`m=(y_(1) -y_(2) )/(x_(1) -x_(2) ) \\\\m=(-4--2)/(-6--3) \\\\m=(-2)/(-3) \\\\m=(2)/(3)`

∴
`y=(2)/(3) x`