Question

What is an equation of the line that passes through the points -5, 1 and 5, -3

Answer 1

y = -
`(2)/(5)` 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 slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

let (x₁, y₁ ) = (- 5, 1 ) and (x₂, y₂ ) = (5, - 3 )

substitute these values into the formula for m

m =
`(-3-1)/(5-(-5))` =
`(-4)/(5+5)` =
`(-4)/(10)` = -
`(2)/(5)` , then

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

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

using (5, - 3 ) for x and y in the partial equation

- 3 = -
`(2)/(5)` (5) + c = - 2 + c ( add 2 to both sides )

- 1 = c

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