Question

Which of the following equations correctly describes the graphed line?

y = 2/3x - 2


y = -2/3x - 2


y = 2/3x + 2


y = -2/3x + 2

Answer 1

y = -
`(2)/(3)` x - 2

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 gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0 , - 2 ) and (x₂ , y₂ ) = A( 6 , - 6 )

m =
`(- 6+ 2)/(6 - 0)` =
`(-4)/(6)` = -
`(2)/(3)`

y -intercept c = - 2 ( from graph )

y = -
`(2)/(3)` x - 2