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3 years ago

Write the equation of a line perpendicular to 9xplus7yequals6 that passes through the point (9,negative 7).

Mathematics

1 answer:

andrew11 [14]3 years ago

7 0

$k:\ y=m_1x+b_1\\\\l:\ y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1$

We have:

$k:\ 9x+7y=6\ \ \ |-9x\\\\7y=-9x+6\ \ \ \ |:7\\\\y=-\dfrac{9}{7}x+\dfrac{6}{9}\to m_1=-\dfrac{9}{7}\\\\l:\ y=m_2x+b\\\\l\ \perp\ k\iff-\dfrac{9}{7}m_2=-1\ \ \ \ |\cdot\left(-\dfrac{7}{9}\right)\\\\m_2=\dfrac{7}{9}\to\ l:\ y=\dfrac{7}{9}x+b$

We know. The line l passes throught the point (9, -7). Substitute the coordinates of the poin to the equation of line l :

$-7=\dfrac{7}{9}\cdot9+b\\\\-7=7+b\ \ \ \ |-7\\\\b=-14$

$y=\dfrac{7}{9}x-14\ \ \ \ |\cdot9\\\\9y=7x-126\ \ \ \ |-9y\ |+126\\\\7x-9y=126$

Answer: $y=\dfrac{7}{9}x-14\to7x-9y=126$

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3 years ago

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2 years ago

3/8 <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B8%7D%20%28x%20-%201%29%28x%20-%209%29" id="TexFormula1" title=" \fr

Verdich [7]

The first step for solving this expression is to distribute $\frac{3}{8}$ through the first set of parenthesis.
$( \frac{3}{8}x - \frac{3}{8})$ × (x - 9)
Now use the FOIL method to multiply each term in the first parenthesis by each term in the second parenthesis. This will look like the following:
$\frac{3}{8}$ x × x - $\frac{3}{8}$ x × 9 - $\frac{3}{8}$ x - $\frac{3}{8}$ × (-9)
Remember that multiplying two negatives together equals a positive,, so the expression changes to:
$\frac{3}{8}$ x × x - $\frac{3}{8}$ x × 9 - $\frac{3}{8}$ x + $\frac{3}{8}$ × 9
Calculate the product of all of the sets of multiplication to make the expression become:
$\frac{3}{8}$ x² - $\frac{27}{8}$ x - $\frac{3}{8}$ x + $\frac{27}{8}$
Lastly,, calculate the difference of - $\frac{27}{8}$ x - $\frac{3}{8}$ x to find your final answer.
$\frac{3}{8}$ x² - $\frac{15}{4}$ x + $\frac{27}{8}$
Let me know if you have any further questions.
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3 years ago

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alexandr1967 [171]

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3 years ago

Write the equation of a line perpendicular to 9xplus7yequals6 that passes through the point ​(9​,negative 7​).

Write the equation of a line perpendicular to 9xplus7yequals6 that passes through the point (9,negative 7).