SAT Question 3cdbf026: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice A is correct. The value of $k$ can be found using the slope-intercept form of a linear equation, $y=mx+b$, where $m$ is the slope and $b$ is the $y$-coordinate of the $y$-intercept. The equation $ax+ky=6$ can be rewritten in the form $y=-\frac{ax}{k}+\frac{6}{k}$. One of the given points, $(0,-3)$, is the $y$-intercept. Thus, the $y$-coordinate of the $y$-intercept, $-3$, must be equal to $\frac{6}{k}$. Multiplying both sides by $k$ gives $-3k=6$. Dividing both sides by $-3$ gives $k=-2$.