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Line A is perpendicular to the line with the equation y = -x/5 and the

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Bunuel
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Line A is perpendicular to the line with the equation y = -x/5 and the [#permalink] New post   13 Jun 2018, 12:12
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Line A is perpendicular to the line with the equation \(y= - \frac{1}{5}x\) and the point (3, -10) is on line A. Which of the following is the equation of line A?


A. \(y=- \frac{1}{5} x - \frac{47}{5}\)

B. \(y = \frac{1}{5} x -\frac{53}{5}\)

C. \(y = 5x\)

D. \(y=5x - 5\)

E. \(y=5x - 25\)
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Re: Line A is perpendicular to the line with the equation y = -x/5 and the [#permalink] New post   13 Jun 2018, 13:43
E

Slope is 5
Point on the line is (3, -10)
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Re: Line A is perpendicular to the line with the equation y = -x/5 and the [#permalink] New post   13 Jun 2018, 22:48
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Solution



Given:
    • Line A is perpendicular to the line with the equation y = \(\frac{-1}{5}\)x
    • The point (3, -10) is on line A

To find:
    • The equation of line A

Approach and Working:
    • The slope of the line y = \(\frac{-1}{5}\)x is (\(\frac{-1}{5}\))

If the slope of line A is m,
    • (\(\frac{-1}{5}\)) m = -1
    Or, m = 5

As line A is passing through the point (3, -10), we can write
    • y = 5x + c
    Or, -10 = 5*3 + c
    Or, c = -10 – 15 = -25

Therefore, the equation of line A:
    • y = 5x – 25

Hence, the correct answer is option E.

Answer: E
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Line A is perpendicular to the line with the equation y = -x/5 and the [#permalink] New post   14 Jun 2018, 08:00
Bunuel wrote:
Line A is perpendicular to the line with the equation \(y= - \frac{1}{5}x\) and the point (3, -10) is on line A. Which of the following is the equation of line A?


A. \(y=- \frac{1}{5} x - \frac{47}{5}\)

B. \(y = \frac{1}{5} x -\frac{53}{5}\)

C. \(y = 5x\)

D. \(y=5x - 5\)

E. \(y=5x - 25\)


Equation of a line passing through point (x,y) and having slope m is:-

y=m*x+c, where c is the y intercept.------------------(1)

Since this line is perpendicular to the line with the equation \(y= - \frac{1}{5}x\),

hence slope of the desired line: m*\(\frac{-1}{5}\)=-1 or m=5.

Since the desired line passes through point(3,-10), hence this point must satisfy eq(1), we have

-10=5*3+c or c=-25.

So, the desired equation of line is:

y=5x-25

Ans. (E)
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Re: Line A is perpendicular to the line with the equation y = -x/5 and the [#permalink] New post   14 Jun 2018, 13:06
Bunuel wrote:
Line A is perpendicular to the line with the equation \(y= - \frac{1}{5}x\) and the point (3, -10) is on line A. Which of the following is the equation of line A?


A. \(y=- \frac{1}{5} x - \frac{47}{5}\)

B. \(y = \frac{1}{5} x -\frac{53}{5}\)

C. \(y = 5x\)

D. \(y=5x - 5\)

E. \(y=5x - 25\)



Given Line A is perpendicular to \(y= - \frac{1}{5}x\).

Since product slopes of two perpendicular lines = \(-1\), we have

Slope of line A \(* (-1/5) = -1\)

Hence slope of line A \(= 5\)

Given that point \((3,-10)\) is on line A, we can

Using the equation of line as \((y-y_1) = m(x-x_1)\) , where \(m = 5\) & \(x_1 = 3\), \(y_1 = -10\)

we get, \((y + 10) = 5*(x - 3)\)

Equation of line A is \(y=5x - 25\)

Answer E.


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GyM
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Re: Line A is perpendicular to the line with the equation y = -x/5 and the [#permalink]
14 Jun 2018, 13:06
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