Answer:
Option C is correct.
Equation of a line [tex]y=\frac{-2}{3}x+6[/tex] passing through (0,6) and (9,0).
Explanation:
Given the two points (0, 6) and (9 ,0).
To find the equation for the given two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is,
[tex]y-y_{1}=m(x-x_{1})[/tex]; where m is the slope and is given by:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
First find the slope m:
[tex]m=\frac{0-6}{9-0} =\frac{-6}{9} =\frac{-2}{3}[/tex]
Substitute this value in equation of line:
[tex]y-6=\frac{-2}{3} (x-0)[/tex] or
[tex]y-6=\frac{-2}{3} x[/tex]
⇒ [tex]y=\frac{-2}{3}x+6[/tex]
Therefore, the equation for the given point is: [tex]y=\frac{-2}{3}x+6[/tex]
