Question

Write an equation of the line containing the given point and perpendicular to the given line. ?(0?,2?); 9x+2y=3

Answer 1

Answer:

The required equation is $y=\frac{2}{9}x+2$.

Step-by-step explanation:

The equation of the given line is

$9x+2y=3$

If a line is defined as $ax+by=c$, then slope of the line is

$m=\frac{-a}{b}$

In the given equation a=9 and b=2. Slope of the line is

$m_1=\frac{-9}{2}$

Product of slopes of two perpendicular line is -1.

Let the slope of required line be $m_2$.

$m_1\times m_2=-1$

$\frac{-9}{2}\times m_2=-1$

$m_2=\frac{2}{9}$

Slope of required line is $\frac{2}{9}$ 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

$y=mx+b$

where, m is slope and b is y-intercept.

Substitute m=2/9 and b=2 in the above equation.

$y=\frac{2}{9}x+2$

Therefore the required equation is $y=\frac{2}{9}x+2$.