SAT Question 00723d16: Linear Equations In Two Variables answer and explanation with Desmos solution

For an equation in slope-intercept form $y=mx+b$, $m$ represents the slope of the line in the xy-plane defined by this equation. It's given that line $l$ is defined by $3y+12x=5$. Subtracting $12x$ from both sides of this equation yields $3y=-12x+5$. Dividing both sides of this equation by $3$ yields $y=-\frac{12}{3}x+\frac{5}{3}$, or $y=-4x+\frac{5}{3}$. Thus, the slope of line $l$ in the xy-plane is $-4$. Since line $n$ is perpendicular to line $l$ in the xy-plane, the slope of line $n$ is the negative reciprocal of the slope of line $l$. The negative reciprocal of $-4$ is $-\frac{1}{\left(-4\right)}=\frac{1}{4}$. Note that 1/4, .25, .250, and 0.25 are examples of ways to enter a correct answer.