Question

Write a linear function ƒ with ƒ(0) = 2 and ƒ(5) = −3

Answer 1

f(x) = - x + 2

Explanation:

the equation of a linear function in slope- intercept form is

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

f(0) = 2 means y = 0 when x = 2 and f(5) = - 3 means y = - 3 when x = 5

thus there are 2 points (2, 0 ) and (5, - 3 )

calculate m using the slope formula

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

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (5, - 3 )

m =
`(-3-2)/(5-0)` =
`(-5)/(5)` = - 1

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

then

f(x) = - x + 2