Sure! Let's solve this problem step by step.
1. Identify the y-Intercept (c):
The y-intercept of the line is where the line crosses the y-axis. This value is given as 2.
2. Determine the Slope (m):
The slope of a line is the tangent of the angle it makes with the x-axis. Here, the tangent of the angle is given as [tex]\(\frac{1}{4}\)[/tex].
Therefore, the slope [tex]\( m = \frac{1}{4} \)[/tex].
3. Form the Equation of the Line:
The standard form of the equation of a line in slope-intercept form is:
[tex]\[
y = mx + c
\][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the y-intercept.
Substitute the given values of [tex]\( m \)[/tex] and [tex]\( c \)[/tex] into this form:
[tex]\[
y = \frac{1}{4}x + 2
\][/tex]
Hence, the equation of the straight line is:
[tex]\[
y = 0.25x + 2
\][/tex]
This is the desired equation of the line that cuts off an intercept of 2 from the y-axis and is inclined at an angle such that [tex]\(\tan\)[/tex] of the angle is [tex]\(\frac{1}{4}\)[/tex] with the x-axis.
