2.1 Find the slope of a linear function w67 The equation of line \( d \) is \( y=\frac{9}{7} x+7 \). Line e is perpendicular to \( d \). What is the slope of line e? Simplify your answer and write it as a proper fraction, improper fraction, or integer.

**Step 1: Identify the slope of line \( d \)** The equation of line \( d \) is given by \[ y=\frac{9}{7}x+7 \] The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope. From the equation, the slope of line \( d \) is \[ m_d = \frac{9}{7} \] **Step 2: Determine the slope of a perpendicular line** If two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other. Therefore, the slope \( m_e \) of line \( e \), which is perpendicular to line \( d \), is given by \[ m_e = -\frac{1}{m_d} = -\frac{1}{\frac{9}{7}} \] Simplifying the negative reciprocal, we get \[ m_e = -\frac{7}{9} \] **Final Answer:** The slope of line \( e \) is \[ -\frac{7}{9} \]