Question

complete the point - slope equation of the line through (6, 4) and (7, 2). use exact numbers.
y - 2 =

Explanation:

Step1: Find the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1, y_1)=(6, 4)\) and \((x_2, y_2)=(7, 2)\). So, \( m=\frac{2 - 4}{7 - 6}=\frac{-2}{1}=-2 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We are using the point \((7, 2)\), so \( y_1 = 2\) and \( x_1 = 7\), and \( m=-2 \). Substituting these values into the point - slope form, we get \( y - 2=-2(x - 7) \). In the given equation \( y - 2=\square\), the right - hand side should be \(-2(x - 7)\).

Answer:

\(-2(x - 7)\)