Question

Find an equation of the linear function given h(1)=6 and h(4)=-3

Answer 1

h(x) = -3x + 9

h(1) = 6 means y = 6 when x = 1

thus 2 points on the line are (1, 6) and (4, - 3)

the equation of a line in ' slope- intercept form ' is

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

to find m use the ' gradient formula '

m = (y₂ - y₁)/(x₂ - x₁) = ( - 3 - 6)/(4 - 1) = (-9)/3 = - 3

partial equation is y = - 3x + c

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

using (1, 6)

6 = - 3 + c ⇒ c = 6 + 3 =9

linear equation is h(x) = - 3x + 9