Question

PLEASE HELP

Answer 1

Answer:

$\large\boxed{1)\ y=\dfrac{2}{3}x+\dfrac{5}{2}}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

Let

$k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have

$2y+3x=1$

Convert to the slope-intercept from:

$2y+3x=1$             subtract 3x from both sides

$2y=-3x+1$            divide both sides by 2

$y=-\dfrac{3}{2}x+\dfrac{1}{2}$

$m_1=-\dfrac{3}{2}\to m_2=-\dfrac{1}{-\frac{3}{2}}=\dfrac{2}{3}$

Therefore your answer is

$1)\ y=\dfrac{2}{3}x+\dfrac{5}{2}$