Question

Use the table to write a linear function that relates y to x.

Answer 1

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

Explanation:

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

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

Calculate m using the slope formula

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

with (x₁, y₁ ) = (- 8, 2) and (x₂, y₂ ) = (1, - 4) ← 2 ordered pairs from the table

m =
`(-4-2)/(1-(-8))` =
`(-6)/(1+8)` =
`(-6)/(9)` = -
`(2)/(3)`

the ordered pair (0, 0 ) indicates the line crosses through the origin, then

c = 0

y = -
`(2)/(3)` x + 0 , that is

y = -
`(2)/(3)` x ← equation of linear function