Question

complete the point - slope equation of the line through (2, 3) and (7, 4). use exact numbers.

$y - 4 = \square$

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, \((x_1, y_1)=(2, 3)\) and \((x_2, y_2)=(7, 4)\). So \( m=\frac{4 - 3}{7 - 2}=\frac{1}{5} \).

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 \((7, 4)\), so substituting \( y_1 = 4 \), \( x_1 = 7 \) and \( m=\frac{1}{5} \) into the point - slope formula, we get \( y - 4=\frac{1}{5}(x - 7) \).

Answer:

\(\frac{1}{5}(x - 7)\)