SAT Question deee9063: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice A is correct. An equation that defines a line in the xy-plane can be written as $y=mx+b$, where $m$ is the slope of the line and $(0,b)$ is its y-intercept. It’s given that line $k$ is defined by the equation $y=6x+4$; therefore, the slope of line $k$ is $6$. Since line $j$ is parallel to line $k$ in the xy-plane and parallel lines have equal slopes, it follows that the slope of line $j$ is $6$. It’s also given that line $j$ passes through the point $(0,5)$, which is its y-intercept. Substituting $6$ for $m$ and $5$ for $b$ in the equation $y=mx+b$ yields $y=6x+5$. Therefore, the equation $y=6x+5$ defines line $j$.