Option C
[tex]\text{The line } y=\frac{-1}{3}x+4 \text { passes through } (3, 3)[/tex]
Solution:
Given that line is:
[tex]y = \frac{-1}{3}x + 4[/tex]
Let us check the options one by one
Option A
(1, -4)
Substitute x = 1 and y = -4
[tex]-4 = -\frac{1}{3} \times 1 + 4\\\\-4 = \frac{-1+12}{3}\\\\-12 = -1 + 12\\\\-12\neq 11[/tex]
Thus the line does not passes through (1, -4)
Option B
(6, 4)
Substitute x = 6 and y = 4
[tex]4= \frac{-1}{3} \times 6+4\\\\-4 = -2 + 4\\\\-4\neq 2[/tex]
Thus the line does not passes through (6, 4)
Option C
(3, 3)
Substitute x = 3 and y = 3
[tex]3 = \frac{-1}{3} \times 3 + 4\\\\3 = -1 + 4\\\\3 = 3[/tex]
Thus the line does not passes through (3, 3)
Option D
(0, -1)
Substitute x = 0 and y = -1
[tex]-1 = \frac{-1}{3} \times 0 + 4\\\\-1\neq 4[/tex]
Thus the line does not pass through this point
