Question

Write the rule for the linear function. Remember a function rule is written using f(x).

Answer 1

f(x) =
`(1)/(5)` x + 1

Explanation:

the equation of a linear function has the form

y = mx + c ( m is the slope and c the y- intercept )

calculate the slope m, using the slope formula

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

let (x₁, y₁ ) = (- 10, - 1) and (x₂, y₂ ) = (10, 3) ← 2 ordered pairs from the table

substitute these values into the formula for m

m =
`(3-(-1))/(10-(-10))` =
`(3+1)/(10+10)` =
`(4)/(20)` =
`(1)/(5)`

the ordered pair (0, 1 ), means the line crosses the y- axis at c = 1

y =
`(1)/(5)` x + 1 , that is expressed as a function

f(x) =
`(1)/(5)` x + 1 ← rule for linear function