Question

Write an equation of the line.
(-2,5)
(5,-2)

Answer 1

y = - x + 3

Explanation:

the equation of a line in slope- intercept form is

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

calculate the slope m using the slope formula

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

let (x₁, y₁ ) = (- 2, 5 ) and (x₂, y₂ ) = (5, - 2 )

substitute these values into the formula for m

m =
`(-2-5)/(5-(-2))` =
`(-7)/(5+2)` =
`(-7)/(7)` = - 1 , then

y = - x + c ← is the partial equation

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

using (- 2, 5 ) for x and y in the partial equation

5 = - (- 2) + c = 2 + c ( subtract 2 from both sides )

3 = c

y = - x + 3 ← equation of line