Question

Please find the equation of the line that goes through the point (5,-10) and (2,8)

Answer 1

y = - 6x + 20

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) )`

with (x₁, y₁ ) = (5, - 10 ) and (x₂, y₂ ) = (2, 8 )

m =
`(8-(-10))/(2-5)` =
`(8+10)/(-3)` =
`(18)/(-3)` = - 6 , then

y = - 6x + c ← is the partial equation

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

using (2, 8 ) , then

8 = - 12 + c ⇒ c = 8 + 12 = 20

y = - 6x + 20 ← equation of line