Does the point $(3,-2)$ satisfy the equation $5x+y=13$? Show your algebraic check and conclusion.

Yes — visually, the point $(3,-2)$ sits on the line defined by the equation because all plotted integer points less than $5$ and greater than $-3$ satisfy similar linear patterns without substitution.

Yes — substituting gives $5\cdot 3+(-2)=13$, which equals the right-hand side, so the point satisfies the equation.

No — substitution yields $5\cdot 3+(-2)=13$, but because $y$ is negative, the point lies below the $x$-axis and cannot satisfy an equation with positive constants.

No — substitution yields $15-2=13$, which is close, but equality requires rounding considerations when plotting by hand on standard graph paper.