Question

Write the equation of the line between the two-points.
Points (-5,-2) and (15,-10)

Answer 1

y = -
`(2)/(5)` x - 4

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 ) = (- 5, - 2 ) and (x₂, y₂ ) = (15, - 10 )

substitute these values into the formula for m

m =
`(-10-(-2))/(15-(-5))` =
`(-10+2)/(15+5)` =
`(-8)/(20)` = -
`(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, - 2 ) for x and y

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

- 4 = c

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