Given:
[tex]y=-\frac{x}{3}-1[/tex]We have the graph below:
To determine the correct ordered pairs, let's solve for each of them.
a) (x, y) ==> (0, -1)
From the equation, substitute 0 for x and -1 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -1=-\frac{0}{3}-1 \\ \\ -1=0-1 \\ \\ -1=-1 \\ \\ \text{Therefore (0, -1) is a solution} \end{gathered}[/tex]b) (x, y) ==> (3, -2)
Substitute 3 for x and -2 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -2=-\frac{3}{3}-1 \\ \\ -2=-1-1 \\ \\ -2=-2 \\ \\ (3,\text{ -2) is a solution} \end{gathered}[/tex]c) (x, y) ==> (3, -5)
Substitute 3 for x and -5 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -5=-\frac{3}{3}-1 \\ \\ -5=-1-1 \\ \\ -5=-2 \\ \\ (3,\text{ -5) is not a solution} \end{gathered}[/tex]d) (0, -5)
Substitute 0 for x and -5 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ -5=-\frac{0}{3}-1 \\ \\ -5=0-1 \\ \\ -5=-1 \\ \\ (0,\text{ -5) is not a solution} \end{gathered}[/tex]e) (x, y) ==> (-3, 0)
Substitute -3 for x and 0 for y:
[tex]\begin{gathered} y=-\frac{x}{3}-1 \\ \\ 0=-\frac{-3}{3}-1 \\ \\ 0=1-1 \\ \\ 0=0 \\ \\ \text{The ordered pair (-3, 0) is a solution} \end{gathered}[/tex]ANSWER:
(0, -1)
(3, -2)
(-3, 0)
