Is it right
1 answer:
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Given the speed is 200 km /hr
use 1 km = 1000 meter
1 hr = 3600 seconds
so
simplifies to
so option C
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:
<em>(Just divide both sides by y)</em>
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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
<em>Note: negative reciprocal means we just flip the fraction and put a minus sign.</em>
The regular gradient is:
So the perpendicular gradient is the negative reciprocal of
which is -5 <em> (note: is just 5-)</em>
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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 <em>(substitute in all known values)</em>
0 = -5(-1) + c <em> (the -1 times -5 will make + 5)</em>
0 = 5 + c <em>(subtract 5 from both sides to cancel out the + 5)</em>
-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 <em>(substitute in the perp. gradient and c)</em>
y = -5x - 5
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<h2>Answer:</h2>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) <em>(Substitute in values)</em>
y - 0 = -5 ( x - - 1) <em>(simplify)</em>
y = -5 (x + 1) <em>(expand the brackets)</em>
y = -5x - 5