Answer:
[tex]\large\boxed{y=5x+2}[/tex]
Step-by-step explanation:
[tex]\text{Let:}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\\text{then}\\\\k\ ||\ l\iff m_1=m_2\\\\k \perp l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\==================================[/tex]
[tex]\text{We have the equation of a line:}\\\\y=-\dfrac{1}{5}x+4\to m_1=-\dfrac{1}{5}\\\\\text{Therefore}\\\\m_2=-\dfrac{1}{-\frac{1}{5}}=-\left(-\dfrac{5}{1}\right)=5\\\\\text{Initially, our equation has the form}\\\\y=5x+b[/tex]
[tex]\text{The line should pass through point (-1, -3).}\\\text{We substitute the coordinates of the point into the equation:}\\\\-3=5(-1)+b\\-3=-5+b\qquad\text{add 5 to both sides}\\-3+5=-5+5+b\\2=b\to b=2\\\\\text{Finally:}\\\\y=5x+2[/tex]
