Question

4. Write the function of a linear equation that includes the
points (1,3) and (2,9).

Answer 1

y = 6x - 3

Explanation:

the equation of a line in slope- intercept form ( linear function ) 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 ) = (1, 3 ) and (x₂, y₂ ) = (2, 9 )

m =
`(9-3)/(2-1)` =
`(6)/(1)` = 6 , then

y = 6x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 3 ) , then

3 = 6 + c ⇒ c = 3 - 6 = - 3

y = 6x - 3 ← equation of linear function