The equation of a line is given as $13y - 5 = 2x$. The problem asks to find the y-intercept of this line.

1. Problem Description

The equation of a line is given as $13y - 5 = 2x$. The problem asks to find the y-intercept of this line.

2. Solution Steps

To find the y-intercept, we need to rewrite the given equation in the slope-intercept form, which is:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

First, we want to isolate the term with $y$ on one side of the equation:

$13y - 5 = 2x$

Add $5$ to both sides:

$13y = 2x + 5$

Now, divide both sides by $13$ to solve for $y$:

$y = \frac{2x + 5}{13}$

$y = \frac{2}{13}x + \frac{5}{13}$

Comparing this with the slope-intercept form $y = mx + b$, we can identify the y-intercept $b$:

$b = \frac{5}{13}$

3. Final Answer

The y-intercept of the line is $\frac{5}{13}$.