Question

I need to find the linear function

Answer 1

y =
`(1)/(2)` x + 7

Explanation:

the equation of a line in slope- intercept form is

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (2, 8) and (x₂, y₂ ) = (10,12) ← 2 ordered pairs from the table

m =
`(12-8)/(10-2)` =
`(4)/(8)` =
`(1)/(2)`

y =
`(1)/(2)` x + c ← is the partial equation

to find c substitute any ordered pair into the partial equation

using (6, 10 ), then

10 = 3 + c ⇒ c = 10 - 3 = 7

y =
`(1)/(2)` x + 7 ← linear equation