Answer:
[tex]y=-5x+22[/tex]
Step-by-step explanation:
If two lines are perpendicular to each other, the product of their slopes will be -1.
Therefore, the slope (m) of the line that is perpendicular to [tex]y=\dfrac{1}{5}x-3[/tex] is:
[tex]\begin{aligned}\implies m \cdot \dfrac{1}{5} & =-1\\m & =-5\end{aligned}[/tex]
Using the point-slope form of a linear equation, with the given point (4, 2) and the calculated slope of -5:
[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\\implies y-2 & = -5(x-4)\\y-2 & = -5x+20\\y & = -5x+22\end{aligned}[/tex]
Therefore, the equation of a line that passes through the point (4, 2) and is perpendicular to the line [tex]y=\dfrac{1}{5}x-3[/tex] is:
[tex]\Large \boxed{y=-5x+22}[/tex]
