Question

DETAILS equation of the line passin (2,1),(-2,-2)

Answer 1

y =
`(3)/(4)` x -
`(1)/(2)`

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) )`

let (x₁, y₁ ) = (2, 1 ) and (x₂, y₂ ) = (- 2, - 2 )

substitute these values into the formula for m

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

y =
`(3)/(4)` x + c ← is the partial equation

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

using (2, 1 )

1 =
`(3)/(4)` (2) + c =
`(3)/(2)` + c ( subtract
`(3)/(2)` from both sides )

`(2)/(2)` -
`(3)/(2)` = c , so c = -
`(1)/(2)`

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