Answer:
[tex]\large\boxed{y=3x}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m\ -\ slope\\b\ -\ y-intercept[/tex]
[tex]\text{Let}\\\\k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2\\====================[/tex]
[tex]\text{We have:}\\\\k:-\dfrac{2}{3}x-2y=-2\\\\\text{Convert to the slope-intercept form}:\\\\-\dfrac{2}{3}x-2y=-2\qquad\text{multiply both sides by 3}\\\\-2x-6y=-6\qquad\text{divide both sides by (-2)}\\\\x+3y=3\qquad\text{subtract}\ x\ \text{from both sides}\\\\3y=-x+3\qquad\text{divide both sides by 3}\\\\y=-\dfrac{1}{3}x+1\to m_1=-\dfrac{1}{3}\\\\\text{Calculate the other slope:}\\\\m_1=-\dfrac{1}{-\frac{1}{3}}=3\\\\\text{Put it to the equation of a line:}\\\\y=3x+b[/tex]
[tex]\text{Put the coordinates of the given point (-1, -3) to the equation:}\\\\-3=3(-1)+b\\-3=-3+b\qquad\text{add 3 to both sides}\\0=b\to b=0\\\\\text{Finally:}\\\\y=3x+0\to y=3x[/tex]
