# How do you find the equation, in point slope form, of the line that is perpendicular to the line y=2x-3and passes through the point (1, 2)?

Apr 16, 2018

color(orange)(x + 2y = 5, " is the standard form of the equation"

#### Explanation:

Point Slope Form of equation is $y - {y}_{1} = m \cdot \left(x - {x}_{1}\right)$

Given : $\left({x}_{1} , {y}_{1}\right) = \left(1 , 2\right)$

$y = 2 x - 3$

Above equation is in the form $y = m x + c , w h e r e m = 2$

Slope of line perpendicular to $y = 2 x - 3$ is $= - \frac{1}{m} = - \frac{1}{2}$

$\therefore \left(y - 2\right) = - \left(\frac{1}{2}\right) \cdot \left(x - 1\right)$

$2 y - 4 = - x + 1$

color(orange)(x + 2y = 5, " is the standard form of the equation"