To see if a pair of points (x, y) lies on the graph of the function 7x - 6y = 1, we need to evaluate each ordered pair in the equation:
[tex]7x-6y=1[/tex]a. (-1, 4):
[tex]\begin{gathered} 7(-1)-6\cdot4=1 \\ -7-24=1 \\ -31\ne1 \end{gathered}[/tex]a is not the answer:
b. (2, 9):
[tex]\begin{gathered} 7\cdot2-6\cdot9=1 \\ 14-54=1 \\ -40\ne1 \end{gathered}[/tex]b is not the answer.
c. (-2, -7)
[tex]\begin{gathered} 7(-2)-6(-7)=1 \\ -14+42=1 \\ 28\ne1 \end{gathered}[/tex]c is not the answer.
d. (3, 7):
[tex]\begin{gathered} 7\cdot3-6\cdot7=1 \\ 21-42=1 \\ -21\ne1 \end{gathered}[/tex]d is not the answer.
e. (1, 1)
[tex]\begin{gathered} 7\cdot1-6\cdot1=1 \\ 7-6=1 \\ 1=1 \end{gathered}[/tex]Thus, the answer is option e. (1, 1)
