Answer: The value of the y-intercept of the line is [tex]-\dfrac{3}{5}.[/tex]
Step-by-step explanation: Given that a line has a slope of [tex]\frac{1}{4}[/tex] and passes through the point [tex](0.4,\frac{1}{2}).[/tex]
We are to find the value of the y-intercept of the line.
The SLOPE-INTERCEPT form of the equation of a straight line is given by
[tex]y=mx+c,[/tex] where m is the slope and c is the y-intercept of the line.
According to the given information, the slope of the given line is
[tex]m=\dfrac{1}{4}.[/tex]
Since the line passes through the point [tex](0.4,\frac{1}{2}),[/tex] so its equation will be
[tex]y-\left(-\dfrac{1}{2}\right)=m(x-0.4)\\\\\\\Rightarrow y+\dfrac{1}{2}=\dfrac{1}{4}\left(x-\dfrac{2}{5}\right)\\\\\\\Rightarrow y=\dfrac{x}{4}-\dfrac{1}{10}-\dfrac{1}{2}\\\\\\\Rightarrow y=\dfrac{x}{4}-\dfrac{1+5}{10}\\\\\\\Rightarrow y=\dfrac{x}{4}-\dfrac{6}{10}\\\\\\\Rightarrow y=\dfrac{x}{4}-\dfrac{3}{5}\\\\\\\Rightarrow y=\dfrac{x}{4}+\left(-\dfrac{3}{5}\right).[/tex]
Comparing with the slope-intercept form, we find that the y-intercept of the line is given by
[tex]c=-\dfrac{3}{5}.[/tex]
Thus, the value of the y-intercept of the line is [tex]-\dfrac{3}{5}.[/tex]
