Question

Find an equation for the line below.

Answer 1

y =
`(4)/(5)` x +
`(6)/(5)`

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 ) = (- 4, - 2) and (x₂, y₂ ) = (6, 6) ← 2 points on the line

m =
`(6-(-2))/(6-(-4))` =
`(6+2)/(6+4)` =
`(8)/(10)` =
`(4)/(5)` , then

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

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

using (6, 6 ) , then

6 =
`(24)/(5)` + c ⇒ c =
`(30)/(5)` -
`(24)/(5)` =
`(6)/(5)`

y =
`(4)/(5)` x +
`(6)/(5)` ← equation of line