Question

Find an equation of a line containing the points (-6,1) and (2,-5).

Answer 1

y = -
`(3)/(4)` x -
`(7)/(2)`

the equation of a line in slope- intercept form is

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 6, 1 ) and (x₂, y₂ ) = (2, - 5 )

m =
`(-5-1)/(2+6)` =
`(-6)/(8)` = -
`(3)/(4)`

the partial equation is

y = -
`(3)/(4)` x + c

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

using (- 6, 1 ), then

1 =
`(9)/(2)` + c ⇒ c = 1 -
`(9)/(2)` = -
`(7)/(2)`

y = -
`(3)/(4)` x -
`(7)/(2)` ← equation of line