Question

The function rule for this graph is

Answer 1

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

Explanation:

The equation of a line in slope- intercept form is

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

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m =
`(0-2)/(4-0)` =
`(-2)/(4)` = -
`(1)/(2)`

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

y = -
`(1)/(2)` x + 2 ← function rule