Question

What is an equation of the line that passes through the point (-6,7) and is perpendicular to the line

Answer 1

The equation of line perpendicular to given line through (-6,7) is:

$y=\frac{1}{6}x+8$

Further explanation:

Given equation of line is:

$6x+y=3\\y= -6x+3$

The co-efficient of x is the slope of given line.

Let m1 be the slope of given line

and

m2 be the slope of line perpendicular to given line

Then

$m_1=-6$

Product of slopes of perpendicular lines is -1

$m_1*m_2 = -1\\-6*m_2=-1\\m_2=\frac{-1}{-6}\\m_2=\frac{1}6}$

The equation of new line can be written as:

$y=m_2x+b$

Putting m2

$y=\frac{1}{6}x+b$

To find the value of b, we will put (-6,7) in equation

$7=\frac{1}{6}(-6)+b\\7=-1+b\\b=7+1\\b=8$

Putting the values of b and m in general equation

$y=\frac{1}{6}x+8$

Keywords: Slope, Point-slope form, perpendicular lines

Learn more about perpendicular lines at:

• brainly.com/question/12941985
• brainly.com/question/4152194

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