91Ó°ÊÓ

First, we rearrange the line equation into a slope-intercept form \(y = mx + b\). This is done by solving for \(y\). From this equation, we can then identify the slope \(m\). In case of the given line \(3x + 4y = 7\), arrange this equation into standard form to get \(y = -\frac{3x}{4} + \frac{7}{4}\). Therefore the slope \(m\) of the given line is \(-\frac{3}{4}\).

For a line to be parallel to another, their slopes should be equal. Hence, the equation of the line parallel to the given line passing through the given point is \(y - y1 = m(x - x1)\) where \(m\) is the slope of the original line and \((x1,y1)\) is the point. Filling the given values we get \(y - \frac{7}{8} = -\frac{3}{4}(x + \frac{2}{3})\). Simplifying this we get \(y = -\frac{3}{4}x - \frac{1}{2}\).\nFor a line to be perpendicular, the slope should be the negative reciprocal of the original line. Thus, the slope of the line perpendicular to the original line is \(\frac{4}{3}\). So, the equation of the line perpendicular to the original line passing through the given point is \(y - y1 = m(x - x1)\). Filling the given values we get \(y - \frac{7}{8} = \frac{4}{3}(x + \frac{2}{3})\). Simplifying gives the final equation \(y = \frac{4}{3}x + \frac{29}{24}\).