# How do you write an equation of a line passing through (1,2), perpendicular to 2y+5 = 3x?

Aug 29, 2016

$y = - \frac{2}{3} x + 2 \frac{2}{3}$

#### Explanation:

Re-arrange the equation of the given line: $y = \frac{3}{2} x - \frac{5}{2}$

The slope of this line is : ${m}_{1} = \frac{3}{2}$
The slope of a line perpendicular to this line is:

${m}_{2} = - \frac{2}{3}$

We have the slope and a point, (1,2) which is $\left({x}_{1} , {y}_{1}\right)$

Substitute into the formula:
$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - 2 = - \frac{2}{3} \left(x - 1\right)$

$y = - \frac{2}{3} x + \frac{2}{3} + 2$

The equation is:
$y = - \frac{2}{3} x + 2 \frac{2}{3}$