Question

find the equation of the line perpendicular to $y = -\frac{1}{8}x + 4$ that includes the point $(2, 3)$. give your answer in point - slope form. $y - ? = \square(x - \square)$ point - slope form: $y - y_1 = m(x - x_1)$

Explanation:

Step1: Find the slope of the perpendicular line

The slope of the given line \( y = -\frac{1}{8}x + 4 \) is \( m_1 = -\frac{1}{8} \). The slope of a line perpendicular to it, \( m \), is the negative reciprocal, so \( m = 8 \) (since \( -\frac{1}{8} \times 8 = -1 \)).

Step2: Identify the point \((x_1, y_1)\)

The line passes through the point \((2, 3)\), so \( x_1 = 2 \) and \( y_1 = 3 \).

Step3: Substitute into point - slope form

The point - slope form is \( y - y_1 = m(x - x_1) \). Substituting \( y_1 = 3 \), \( m = 8 \), and \( x_1 = 2 \), we get \( y - 3 = 8(x - 2) \).

Answer:

\( y - 3 = 8(x - 2) \)