Question

which equation represents a line that passes through \\(\left(4, \frac{1}{3}\
ight)\\) and has a slope of \\(\frac{3}{4}\\)?\\(y - \frac{1}{3} = 4\left(x - \frac{3}{4}\
ight)\\)\\(y - \frac{1}{3} = \frac{3}{4}(x - 4)\\)\\(y - 4 = \frac{3}{4}\left(x - \frac{1}{3}\
ight)\\)\\(y - \frac{3}{4} = \frac{1}{3}(x - 4)\\)

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 \((4,\frac{1}{3})\), so \(x_1 = 4\) and \(y_1=\frac{1}{3}\). The slope of the line \(m=\frac{3}{4}\).

Step3: Substitute into point - slope form

Substitute \(x_1 = 4\), \(y_1=\frac{1}{3}\) and \(m = \frac{3}{4}\) into the point - slope form \(y - y_1=m(x - x_1)\). We get \(y-\frac{1}{3}=\frac{3}{4}(x - 4)\).

Answer:

\(y-\frac{1}{3}=\frac{3}{4}(x - 4)\) (the second option)