Question

which equation shows the point - slope form of the line that passes through (3, 2) and has a slope of \\(\frac{1}{3}\\)?\\(y - 3 = \frac{1}{3}(x - 2)\\)\\(y + 2 = \frac{1}{3}(x + 3)\\)\\(y - 2 = \frac{1}{3}(x - 3)\\)\\(y + 3 = \frac{1}{3}(x + 2)\\)

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is given by \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope of the line.

Step2: Identify \(x_1\), \(y_1\) and \(m\)

We are given that the line passes through the point \((3,2)\), so \(x_1 = 3\) and \(y_1=2\). The slope \(m=\frac{1}{3}\).

Step3: Substitute into the formula

Substitute \(x_1 = 3\), \(y_1 = 2\) and \(m=\frac{1}{3}\) into the point - slope formula \(y - y_1=m(x - x_1)\). We get \(y - 2=\frac{1}{3}(x - 3)\).

Answer:

\(y - 2=\frac{1}{3}(x - 3)\) (the third option)