Write an equation of the line that passes through the points (1,1) (5,9)

y = 2x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

To find m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (1, 1) and (x₂, y₂ ) = (5, 9)

m = = = 2

y = 2x + c ← is the partial equation

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

using (1, 1 ), then

1 = 2 + c ⇒ c = 1 - 2 = - 1

y = 2x - 1 ← equation of line