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Passing through (-2,1 ) and perpendicular to
4x + 7y + 3 = 0.

User Arsh
by
7.7k points

1 Answer

2 votes

Answer:

7x - 4y + 18 = 0

Explanation:

The slope-intercept form of an equation of a line:


y=mx+b

m - slope

b - y-intercept

========================================

Let


k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\l\ \parallel\ k\iff m_1=m_2

========================================

We have the equation of a line in a general form (Ax + By + C = 0)

Convert it to the slope-intercept form:


4x+7y+3=0 subtract 7y from both sides


4x+3=-7y divide both sides by (-7)


-(4)/(7)x-(3)/(7)=y\to m_1=-(4)/(7)

Therefore


m_2=-(1)/(-(4)/(7))=(7)/(4)

We have the equation:


y=(7)/(4)x+b

Put the coordinates of the point (-2, 1) to the equation, and solve for b :


1=(7)/(4)(-2)+b


1=-(7)/(2)+b multiply both sides by 2


2=-7+2b add 7 to both sides


9=2b divide both sides by 2

[te]x\dfrac{9}{2}=b\to b=\dfrac{9}{2}[/tex]

Finally:


y=(7)/(4)x+(9)/(2) - slope-intercept form

Convert to the general form:


y=(7)/(4)x+(9)/(2) multiply both sides by 4


4y=7x+18 subtract 4y from both sides


0=7x-4y+18

User Galex
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