sat-dog

The correct answer is $\frac{1}{2}$. 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 $p$ is defined by $4y+8x=6$. Subtracting $8x$ from both sides of this equation yields $4y=-8x+6$. Dividing both sides of this equation by $4$ yields $y=-\frac{8}{4}x+\frac{6}{4}$, or $y=-2x+\frac{3}{2}$. Thus, the slope of line $p$ is $-2$. If line $r$ is perpendicular to line $p$, then the slope of line $r$ is the negative reciprocal of the slope of line $p$. The negative reciprocal of $-2$ is $-\frac{1}{\left(-2\right)}=\frac{1}{2}$. Note that 1/2 and .5 are examples of ways to enter a correct answer.