Question

Find the equation of the line passing
through the points (4, 2) and (6, 10).

Answer 1

y = 4x - 14

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 ) = (4, 2 ) and (x₂, y₂ ) = (6, 10 )

m =
`(10-2)/(6-4)` =
`(8)/(2)` = 4 , then

y = 4x + c ← is the partial equation

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

using (4, 2 ) , then

2 = 16 + c ⇒ c = 2 - 16 = - 14

y = 4x - 14 ← equation of line