SAT Question a7a14e87: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice D is correct. It's given that line $j$ is perpendicular to line $k$ and that line $k$ is defined by the equation $x+y=0$. This equation can be rewritten in slope-intercept form, $y=mx+b$, where $m$ represents the slope of the line and $b$ represents the $y$-coordinate of the $y$-intercept of the line, by subtracting $x$ from both sides of the equation, which yields $y=-x$. Thus, the slope of line $k$ is $-1$. Since line $j$ and line $k$ are perpendicular, their slopes are opposite reciprocals of each other. Thus, the slope of line $j$ is $1$. It's given that the $y$-intercept of line $j$ is $(0,3)$. Therefore, the equation for line $j$ in slope-intercept form is $y=x+3$, which can be rewritten as $x-y=-3$.