Question

Write the equation of the line perpendicular to 2x+3y=9 that passes through (-2,5). Write your answer in slope-intercept form. Show your work.

Answer 1

ANSWER

$y = \frac{3}{2} x + 8$



EXPLANATION

The line given to us has equation,

$2x + 3y = 9$

We need to write this equation in the slope intercept form to obtain,


$3y = - 2x + 9$



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


The slope of this line is

$m_1 = - \frac{2}{3}$
Let the slope of the perpendicular line be

$m_2$

Then
$m_1 \times m_2 = - 1$


$- \frac{2}{3} m_2= - 1$

This implies that,

$m_2 = - 1 \times - \frac{3}{2}$


$m_2 = \frac{3}{2}$



Let the equation of the perpendicular line be,

$y = mx + b$

We substitute the slope to get,


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

Since this line passes through
$(-2,5)$
it must satisfy its equation.


This means that,

$5= \frac{3}{2} ( - 2)+ b$


$5 = - 3 + b$



$5 + 3 = b$


$b = 8$

Wherefore the slope-intercept form is

$y = \frac{3}{2} x + 8$