In the xy -plane, line l passes through the point 0 , 0 and is parallel

The correct answer is $24$. A line in the xy-plane can be defined by the equation $y=mx+b$, where $m$ is the slope of the line and $b$ is the y-coordinate of the y-intercept of the line. It's given that line $\mathcal{l}$ passes through the point $\left(0,0\right)$. Therefore, the y-coordinate of the y-intercept of line $\mathcal{l}$ is $0$. It's given that line $\mathcal{l}$ is parallel to the line represented by the equation $y=8x+2$. Since parallel lines have the same slope, it follows that the slope of line $\mathcal{l}$ is $8$. Therefore, line $\mathcal{l}$ can be defined by an equation in the form $y=mx+b$, where $m=8$ and $b=0$. Substituting $8$ for $m$ and $0$ for $b$ in $y=mx+b$ yields the equation $y=8x+0$, or $y=8x$ . If line $\mathcal{l}$ passes through the point $\left(3,d\right)$, then when $x=3$, $y=d$ for the equation $y=8x$. Substituting $3$ for $x$ and $d$ for $y$ in the equation $y=8x$ yields $d=8\left(3\right)$, or $d=24$.