Question

Choose the equation that represents the graph below: (1 point) Graph of a line passing through points 0 comma 6 and 9 comma 0 y = −2x − 6 y = two thirds x + 6 y = − two thirds x + 6 y = 2x + 6

Answer 1

Option C is correct.

Equation of a line
`y=(-2)/(3)x+6` passing through (0,6) and (9,0).

Step-by-step explanation:

Given the two points (0, 6) and (9 ,0).

To find the equation for the given two points
`(x_(1),y_(1))` and
`(x_(2),y_(2))` is,

`y-y_(1)=m(x-x_(1))`; where m is the slope and is given by:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

First find the slope m:

`m=(0-6)/(9-0) =(-6)/(9) =(-2)/(3)`

Substitute this value in equation of line:

`y-6=(-2)/(3) (x-0)` or

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

⇒
`y=(-2)/(3)x+6`

Therefore, the equation for the given point is:
`y=(-2)/(3)x+6`