Line l is defined by 3 y + 12 x = 5 . Line n is

The correct answer is $\frac{1}{4}$. 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 $\mathcal{l}$ 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 $\mathcal{l}$ in the xy-plane is $-4$. Since line $n$ is perpendicular to line $\mathcal{l}$ in the xy-plane, the slope of line $n$ is the negative reciprocal of the slope of line $\mathcal{l}$. The negative reciprocal of $-4$ is $-\frac{1}{\left(-4\right)}=\frac{1}{4}$. Note that 1/4 and .25 are examples of ways to enter a correct answer.