Question

What is an equation for the line that passes through the coordinates (1, 1) and (3, 5)?

Answer 1

y = 2x - 1

Explanation:

the equation of a line 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 ) = (1, 1 ) and (x₂, y₂ ) = (3, 5 )

m =
`(5-1)/(3-1)` =
`(4)/(2)` = 2 , then

y = 2x + c ← is the partial equation

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

using (1, 1 )

1 = 2 + c ⇒ c = 1 - 2 = - 1

y = 2x - 1 ← equation of line