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