Question

which equation represents a line that passes through (5, 1) and has a slope of \\(\frac{1}{2}\\)?
\\(y - \frac{1}{2} = 5(x - 1)\\)
\\(y - 1 = 5\left(x - \frac{1}{2}\
ight)\\)
\\(y - 1 = \frac{1}{2}(x - 5)\\)
\\(y - 5 = \frac{1}{2}(x - 1)\\)

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.

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

We are given that the line passes through the point \((5,1)\), so \(x_1 = 5\) and \(y_1=1\). The slope of the line \(m=\frac{1}{2}\).

Step3: Substitute into point - slope form

Substitute \(x_1 = 5\), \(y_1 = 1\) and \(m=\frac{1}{2}\) into the point - slope form \(y - y_1=m(x - x_1)\). We get \(y - 1=\frac{1}{2}(x - 5)\).

Answer:

\(y - 1=\frac{1}{2}(x - 5)\) (the third option)