Question

MATH HELP

Answer 1

The equation of line perpendicular to given line is:

$y = \frac{2}{3}x-1$

Step-by-step explanation:

Given equation is:

$3x+2y = -8$

First of all, we have to find the slope of the given line

So,

$3x+2y = -8\\2y = -3x-8$

Dividing both sides by 2

$\frac{2y}{2} = \frac{-3x-8}{2}\\y = \frac{-3x}{2} - \frac{8}{2}\\y =-\frac{3}{2}x-4$

As the equation is in slope-intercept form, the co-efficient of x will be the slope of the line

$m_1 = -\frac{3}{2}$

As we know that product of slopes of two perpendicular lines is -1

Let m-2 be the slope of line perpendicular to given line

$m_1.m_2 = -1\\-\frac{3}{2} . m_2 = -1\\m_2 = -1 * -\frac{2}{3}\\m_2 = \frac{2}{3}$

Slope-intercept form is:

$y = m_2x+b$

putting the value of the slope

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

Putting the point (3,1) in the equation

$1 = \frac{2}{3}(3) +b\\1 = 2 + b\\b = 1-2\\b = -1$

Putting the value of b

$y = \frac{2}{3}x-1$

Hence,

The equation of line perpendicular to given line is:

$y = \frac{2}{3}x-1$

Keywords: Slope-intercept form, slope

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