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:
[tex]5y = x - 5[/tex] (Just divide both sides by y)
[tex]y = \frac{1}{5}x -1[/tex]
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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 [tex]y = \frac{1}{5}x -1[/tex]
Note: negative reciprocal means we just flip the fraction and put a minus sign.
The regular gradient is: [tex]\frac{1}{5}[/tex]
So the perpendicular gradient is the negative reciprocal of [tex]\frac{1}{5}[/tex]
which is -5 (note: [tex]\frac{-5}{1}[/tex] 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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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
