#### Answer

y=$\frac{1}{4}$x+6$\frac{1}{4}$

#### Work Step by Step

Since they are supposed to be perpendicular, the desired line must have a slope that is the opposite of the reciprocal of the slope of the given line, y=-4x+7. The given line is in slope-intercept form, so we know that its slope is -4. Therefore the desired line has a slope of m=$\frac{1}{4}$.
y-y$_1$=m(x-x$_1$)
y-7=$\frac{1}{4}$(x-3)
y-7=$\frac{1}{4}$x-$\frac{3}{4}$
y=$\frac{1}{4}$x+6$\frac{1}{4}$