Answer:
[tex]\large\boxed{1)\ y=\dfrac{2}{3}x+\dfrac{5}{2}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
Let
[tex]k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
We have
[tex]2y+3x=1[/tex]
Convert to the slope-intercept from:
[tex]2y+3x=1[/tex] subtract 3x from both sides
[tex]2y=-3x+1[/tex] divide both sides by 2
[tex]y=-\dfrac{3}{2}x+\dfrac{1}{2}[/tex]
[tex]m_1=-\dfrac{3}{2}\to m_2=-\dfrac{1}{-\frac{3}{2}}=\dfrac{2}{3}[/tex]
Therefore your answer is
[tex]1)\ y=\dfrac{2}{3}x+\dfrac{5}{2}[/tex]
