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blagie [28]
3 years ago
12

Write an equation of the line that passes through the point (6,-2) and is perpendicular to the line 6x+y=2

Mathematics
1 answer:
Scilla [17]3 years ago
8 0

Answer:

y=2x-14

Step-by-step explanation:

Gradient as m(for 1st line m1 and m2 for 2nd line)

m1/m2=-1

m1=(-1)*(-2)=2

y-(-2)/x-6=2

y+2/x-6=2

y+2=2x-12

y=2x-14

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let's recall that in a Kite the diagonals meet each other at 90° angles, Check the picture below, so we're looking for the equation of a line that's perpendicular to BD and that passes through (-1 , 3).

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of BD

y = \stackrel{\stackrel{m}{\downarrow }}{3}x-1\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}

\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{3\implies \cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}

so we're really looking for the equation of a line whose slope is -1/3 and passes through point A

(\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{1}{3}}[x-\stackrel{x_1}{(-1)}]\implies y-3=-\cfrac{1}{3}(x+1) \\\\\\ y-3=-\cfrac{1}{3}x-\cfrac{1}{3}\implies y=-\cfrac{1}{3}x-\cfrac{1}{3}+3\implies y=-\cfrac{1}{3}x+\cfrac{8}{3}

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<h3>What is interest?</h3>

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We know that monthly payments include the interest on the principal amount that is not been paid during the purchase of an item, if the down payment is more than the principal amount that the customer does not pay will decrease which will decrease the loan amount, thus, the interest on the principal amount will decrease as well.

Now, as the interest and the principal amount have both is been reduced, therefore, the monthly instalment(monthly payment) will be reduced as well.

Hence, the correct option is D, A bigger down payment is money paid toward principal, interest-free, which also decreases the amount paid monthly.

Learn more about Interest:

brainly.com/question/2793278

3 0
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Step-by-step explanation:

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