The equation of line perpendicular to given line is:
[tex]y = \frac{2}{3}x-1[/tex]
Step-by-step explanation:
Given equation is:
[tex]3x+2y = -8[/tex]
First of all, we have to find the slope of the given line
So,
[tex]3x+2y = -8\\2y = -3x-8\\[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2} = \frac{-3x-8}{2}\\y = \frac{-3x}{2} - \frac{8}{2}\\y =-\frac{3}{2}x-4[/tex]
As the equation is in slope-intercept form, the co-efficient of x will be the slope of the line
[tex]m_1 = -\frac{3}{2}[/tex]
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
[tex]m_1.m_2 = -1\\-\frac{3}{2} . m_2 = -1\\m_2 = -1 * -\frac{2}{3}\\m_2 = \frac{2}{3}[/tex]
Slope-intercept form is:
[tex]y = m_2x+b[/tex]
putting the value of the slope
[tex]y = \frac{2}{3}x+b[/tex]
Putting the point (3,1) in the equation
[tex]1 = \frac{2}{3}(3) +b\\1 = 2 + b\\b = 1-2\\b = -1[/tex]
Putting the value of b
[tex]y = \frac{2}{3}x-1[/tex]
Hence,
The equation of line perpendicular to given line is:
[tex]y = \frac{2}{3}x-1[/tex]
Keywords: Slope-intercept form, slope
Learn more about equation of line at:
- brainly.com/question/750742
- brainly.com/question/7419893
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