# How do you write the slope-intercept equation for the line that passes through (-2,3) and is perpendicular to 2x-9y=-12?

Jun 25, 2017

Equation of line in slope intercept form is $y = - \frac{9}{2} x - 6$

#### Explanation:

The slope of line $2 x - 9 y = - 12 \mathmr{and} 9 y = 2 x + 12 \mathmr{and} y = \frac{2}{9} x + \frac{4}{3}$ is

${m}_{1} = \frac{2}{9} \therefore {m}_{2} = - \frac{1}{\frac{2}{9}} = - \frac{9}{2}$ since product of perpendicular

lines is unity. Let the equation of line in slope intercept form is

y=m_2x+c or y = -9/2x +c ; (-2,3) is on the line , so it will satisfy the equation.

$\therefore 3 = - \frac{9}{2} \cdot \left(- 2\right) + c \mathmr{and} 3 = 9 + c \mathmr{and} c = 3 - 9 = - 6$

Hence the equation of line in slope intercept form is $y = - \frac{9}{2} x - 6$ [ans]