Question

What is an equation of the line that passes through the points (2,−6) and (−2,4)?

Answer 1

y = -
`(5)/(2)` x - 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 ) = (2, - 6 ) and (x₂, y₂ ) = (- 2, 4 )

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

y = -
`(5)/(2)` x + c ← is the partial equation

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

using (- 2, 4 ) , then

4 = 5 + c ⇒ c = 4 - 5 = - 1

y = -
`(5)/(2)` x - 1 ← equation of line