Question

find the y - intercept of the line $y = \frac{3}{13}x + \frac{1}{5}$. write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.

Explanation:

Step1: Recall the slope - intercept form of a line

The slope - intercept form of a line is given by \(y = mx + b\), where \(m\) is the slope of the line and \(b\) is the \(y\) - intercept. The \(y\) - intercept is the value of \(y\) when \(x = 0\).

Step2: Identify the value of \(b\) in the given equation

In the equation \(y=\frac{3}{13}x+\frac{1}{5}\), comparing it with the slope - intercept form \(y = mx + b\), we can see that \(m=\frac{3}{13}\) and \(b = \frac{1}{5}\). When \(x = 0\), \(y=b\). So the \(y\) - intercept is the constant term in the slope - intercept form of the line equation.

Answer:

\(\frac{1}{5}\)