Question

Line f passes through points (2, 2) and (4, 9). Line g is perpendicular to f. What is the slope of line g?

Answer 1

To determine the slope of line \( g \), we first need to find the slope of line \( f \). The slope \( m \) of a line that passes through points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

For line \( f \), the points are \((2, 2)\) and \((4, 9)\).

Plugging in the points:

\[
m_f = \frac{9 - 2}{4 - 2} = \frac{7}{2}
\]

So, the slope of line \( f \) is \(\frac{7}{2}\).

Since line \( g \) is perpendicular to line \( f\), the slope of line \( g \) (denoted as \( m_g \)) is the negative reciprocal of the slope of line \( f \). The negative reciprocal is found by taking the negative of the reciprocal of \( m_f \):

\[
m_g = -\frac{1}{m_f} = -\frac{1}{\frac{7}{2}} = -\frac{2}{7}
\]

Thus, the slope of line \( g \) is

\[
\boxed{-\frac{2}{7}}.
\]