Answer:
The required equation is [tex]y=\frac{2}{9}x+2[/tex].
Step-by-step explanation:
The equation of the given line is
[tex]9x+2y=3[/tex]
If a line is defined as [tex]ax+by=c[/tex], then slope of the line is
[tex]m=\frac{-a}{b}[/tex]
In the given equation a=9 and b=2. Slope of the line is
[tex]m_1=\frac{-9}{2}[/tex]
Product of slopes of two perpendicular line is -1.
Let the slope of required line be [tex]m_2[/tex].
[tex]m_1\times m_2=-1[/tex]
[tex]\frac{-9}{2}\times m_2=-1[/tex]
[tex]m_2=\frac{2}{9}[/tex]
Slope of required line is [tex]\frac{2}{9}[/tex] and it passes through the point (0,2). It means the y-intercept of the line is 2.
The slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
Substitute m=2/9 and b=2 in the above equation.
[tex]y=\frac{2}{9}x+2[/tex]
Therefore the required equation is [tex]y=\frac{2}{9}x+2[/tex].
