To find the [tex]$y$[/tex]-intercept of the line given by the equation \( y = 4x + \frac{1}{10} \), let's follow these steps:
1. Identify the form of the linear equation:
The equation of a line in slope-intercept form is given by:
[tex]\[
y = mx + b
\][/tex]
where \( m \) represents the slope of the line and \( b \) represents the y-intercept.
2. Match the given equation to the slope-intercept form:
In the given equation \( y = 4x + \frac{1}{10} \), we can compare it directly to \( y = mx + b \).
3. Extract the y-intercept value \( b \) from the equation:
Here, \( b \) is the constant term in the equation. Thus, the y-intercept for the given equation is \( \frac{1}{10} \).
4. Convert the y-intercept into decimal form (if necessary):
Often, it's helpful to represent fractional values in decimal form for clarity. The fraction \( \frac{1}{10} \) translates to the decimal value \( 0.1 \).
Therefore, the y-intercept of the line described by the equation [tex]\( y = 4x + \frac{1}{10} \)[/tex] is [tex]\( 0.1 \)[/tex].
