Question

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

Answer 1

Answer:

7x - 4y + 18 = 0

Step-by-step explanation:

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

$y=mx+b$

m - slope

b - y-intercept

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Let

$k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2$

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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)

$-\dfrac{4}{7}x-\dfrac{3}{7}=y\to m_1=-\dfrac{4}{7}$

Therefore

$m_2=-\dfrac{1}{-\frac{4}{7}}=\dfrac{7}{4}$

We have the equation:

$y=\dfrac{7}{4}x+b$

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

$1=\dfrac{7}{4}(-2)+b$

$1=-\dfrac{7}{2}+b$     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:

$y=\dfrac{7}{4}x+\dfrac{9}{2}$ - slope-intercept form

Convert to the general form:

$y=\dfrac{7}{4}x+\dfrac{9}{2}$         multiply both sides by 4

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

$0=7x-4y+18$