Line g passes through points (6,1) and (9,8) Line h is perpendicular to g. What is the slope of line h? Simplify your answer and write it as a proper fraction, improper fraction, or integer. square

To find the slope of line h, which is perpendicular to line g, we first need to determine the slope of line g.<br /><br />The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:<br />\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]<br /><br />For line g passing through points $(6,1)$ and $(9,8)$, we have:<br />\[ \text{slope of g} = \frac{8 - 1}{9 - 6} = \frac{7}{3} \]<br /><br />Since line h is perpendicular to line g, the slope of line h is the negative reciprocal of the slope of line g. Therefore, the slope of line h is:<br />\[ \text{slope of h} = -\frac{3}{7} \]<br /><br />So, the slope of line h is $\boxed{-\frac{3}{7}}$.