1. The problem states that line e has a slope of $-\frac{34}{43}$ and line f is perpendicular to line e. We need to find the slope of line f. 2. Recall the rule for slopes of perpendicular lines: If two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other. 3. The slope of line e is $m_e = -\frac{34}{43}$. 4. The negative reciprocal of $m_e$ is calculated by flipping the fraction and changing the sign: $$m_f = -\frac{1}{m_e} = -\frac{1}{-\frac{34}{43}}$$ 5. Simplify the expression: $$m_f = -\frac{1}{-\frac{34}{43}} = -\left(-\frac{43}{34}\right) = \frac{43}{34}$$ 6. Therefore, the slope of line f is $\frac{43}{34}$. This fraction is already in simplest form. Final answer: $\boxed{\frac{43}{34}}$