Question

Write the equation of the line that is perpendicular to the line 5y=x−5 through the point (-1,0).

Answer 1

Steps:

---> Re arrange equation to get the format: y = mx + c

---> Work out the perpendicular gradient from the first equation

----> Substitute the x and y coordinates of point (-1, 0) and the perpendicular      gradient into y = mx + c   and work out c

---> Finally, substitute the perpendicular gradient and the value for c into y =mx + c  to get the gradient of the perpendicular line:

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Rearranging equation into the format: y = mx + c:

$5y = x - 5$                  (Just divide both sides by y)

$y = \frac{1}{5}x -1$

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Working out the perpendicular gradient:

To work out the perpendicular gradient, we just take the negative reciprocal of the gradient of $y = \frac{1}{5}x -1$

Note: negative reciprocal means we just flip the fraction and put a minus sign.

The regular gradient is: $\frac{1}{5}$

So the perpendicular gradient is the negative reciprocal of $\frac{1}{5}$

which is -5       (note: $\frac{-5}{1}$ is just 5-)

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Now lets substitute in the values for the gradient (m), the y coord (0) and x coord (-1) of the point (-1, 0)   into y = mx + c, and solve for c:

y = mx + c     (substitute in all known values)

0 = -5(-1) + c   (the -1 times -5 will make + 5)

0 = 5 + c        (subtract 5 from both sides to cancel out the + 5)

-5 = c

so c = -5

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Finally, just substitute in the perpendicular gradient and the value for c into y = mx + c   to get the equation of the perpendicular line:

y = mx + c        (substitute in the perp. gradient and c)

y = -5x - 5

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Answer:

The equation to the line perpendicular to 5y = x - 5 through point (-1, 0) is :

C. y = -5x - 5

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A quicker way to get equation of the perpendicular line once you know the perp. gradient is to use the equation:

y - y1 = m (x - x1)

y1 is the y coordinate of (-1, 0)

x1 is the x coordinate of (-1, 0)

m is the perpendicular gradient.

y - y1 = m (x - x1)       (Substitute in values)

y - 0 = -5 ( x - - 1)       (simplify)

y = -5 (x + 1)              (expand the brackets)

y = -5x - 5