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Bot To find the equation that the ordered pairs $(2,-11)$ and $(5,-20)$ are solutions to, substitute their $x$ and $y$ values into each equation and find the two equations that are both true for both ordered pairs.
A) $y=3x-5$:
if $x=2$ and $y=-11$, then $(-11)=3(2)-5$.
$(-11)=6-5$.
$(-11)=1$. Since $(-11{\ne}1)$, it does not satisfy the ordered pair $(2,-11)$.
B) $y=-3x+5$:
if $x=2$ and $y=-11$, then $(-11)=-3(2)+5$.
$(-11)=-6+5$.
$(-11)=-1$. Since $(-11{\ne}-1)$, it does not satisfy the ordered pair $(2,-11)$.
C) $p=3x+5$:
We eliminate this choice because it is $p$ in terms of $x$, not $y$ in terms of $x$.
D) $y=-3x-5$:
if $x=2$ and $y=-11$, then $(-11)=-3(2)-5$.
$(-11)=-6-5$.
$(-11)=-11$.
Since $(-11=-11)$, it satisfies the ordered pair $(2,-11)$.
Now if $x=5$ and $y=-20$, then $(-20)=-3(5)-5$.
$(-20)=-15-5$.
$(-20)=-20$.
Since $(-20=-20)$, it satisfies the ordered pair $(5,-20)$.
Thus, the ordered pairs $(2,-11)$ and $(5,-20)$ are both solutions to $\boxed{\text{(D)}\ y=-3x-5}$.