Question

what is the equation of the line that passes through the point (6, 2) and has a slope of \\(\frac{1}{3}\\)?

Explanation:

Step1: Recall point - slope form

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.
Here, \(x_1 = 6\), \(y_1=2\) and \(m=\frac{1}{3}\).
Substitute these values into the point - slope formula: \(y - 2=\frac{1}{3}(x - 6)\)

Step2: Simplify the equation

First, distribute the \(\frac{1}{3}\) on the right - hand side:
\(y - 2=\frac{1}{3}x-2\)
Then, add 2 to both sides of the equation to solve for \(y\):
\(y=\frac{1}{3}x-2 + 2\)
\(y=\frac{1}{3}x\)

Answer:

The equation of the line is \(y=\frac{1}{3}x\) (or in standard form \(x - 3y = 0\))