1. **State the problem:** (a) Find the value of $h$ if point $P(h,7)$ lies on the line $3y + 2x = 5$. (b) Find the equation of line $L$ which is perpendicular to $3y + 2x = 5$ and passes through $P$. 2. **Find $h$:** Substitute $y=7$ and $x=h$ into the line equation: $$3(7) + 2h = 5$$ Simplify: $$21 + 2h = 5$$ Subtract 21 from both sides: $$2h = 5 - 21 = -16$$ Divide both sides by 2: $$h = \frac{-16}{2} = -8$$ So, $h = -8$. 3. **Find the equation of line $L$ perpendicular to $3y + 2x = 5$ passing through $P(-8,7)$:** Rewrite the original line in slope-intercept form $y = mx + b$: $$3y = -2x + 5$$ $$y = -\frac{2}{3}x + \frac{5}{3}$$ The slope of the original line is $m = -\frac{2}{3}$. The slope of a line perpendicular to it is the negative reciprocal: $$m_{\perp} = \frac{3}{2}$$ Use point-slope form for line $L$ passing through $(-8,7)$: $$y - 7 = \frac{3}{2}(x + 8)$$ Simplify: $$y - 7 = \frac{3}{2}x + 12$$ Add 7 to both sides: $$y = \frac{3}{2}x + 19$$ **Final answers:** (a) $h = -8$ (b) Equation of line $L$ is $y = \frac{3}{2}x + 19$