Algebra 2 D. 1 Find the slope of a linear function w67 The equation of line \( b \) is \( y=\frac{9}{4} x+4 \). Line \( c \) is perpendicular to \( b \). What is the slope of line \( c \) ? Simplify your answer and write it as a proper fraction, improper fraction, or integer. Submit

To find the slope of line \( c \), we first need to recognize that the slope of line \( b \) is \( \frac{9}{4} \). The slope of a line that is perpendicular to another is the negative reciprocal of that slope. Thus, we take the reciprocal of \( \frac{9}{4} \), which is \( \frac{4}{9} \), and then apply the negative sign. Therefore, the slope of line \( c \) is \( -\frac{4}{9} \). Slope interactions can be visualized in various practical scenarios! For example, imagine trying to design a ramp. If your ramp is set at a slope of \( \frac{9}{4} \) (quite steep!), and you need to construct a railing that runs perpendicular to it for safety, you would need to use that \( -\frac{4}{9} \) slope for the railing to ensure stability. Understanding these relationships is crucial in architecture and construction.