Question

Choose the equation that represents the graph below

Answer 1

y = -
`(2)/(3)` x + 6

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 ) = (0, 6) and (x₂, y₂ ) = (6, 2) ← 2 points on the line

substitute these values into the formula for m

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

the line crosses the y- axis at (0, 6 ) , then c = 6

y = -
`(2)/(3)` x + 6 ← equation of line