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Solution 2.2:5d

From Förberedande kurs i matematik 1

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Current revision (12:44, 24 September 2008) (edit) (undo)
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If two non-vertical lines are perpendicular to each other, their slopes <math>k_{1}</math> and <math>k_{2}</math> satisfy the relation <math>k_{1}k_{2}=-1</math>, and from this we have that the line we are looking for must have a slope that is given by
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<center> [[Bild:2_2_5d-1(2).gif]] </center>
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{{Displayed math||<math>k_{2} = -\frac{1}{k_{1}} = -\frac{1}{2}</math>}}
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<center> [[Bild:2_2_5d-2(2).gif]] </center>
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since the line <math>y=2x+5</math> has a slope <math>k_{1}=2</math>
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(the coefficient in front of ''x'').
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The line we are looking for can thus be written in the form
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{{Displayed math||<math>y=-\frac{1}{2}x+m</math>}}
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with ''m'' as an unknown constant.
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Because the point (2,4) should lie on the line, (2,4) must satisfy the equation of the line,
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{{Displayed math||<math>4=-\frac{1}{2}\cdot 2+m\,,</math>}}
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i.e. <math>m=5</math>. The equation of the line is <math>y=-\frac{1}{2}x+5</math>.
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<center>[[Image:2_2_5d-2(2).gif]]</center>

Current revision

If two non-vertical lines are perpendicular to each other, their slopes k1 and k2 satisfy the relation k1k2=−1, and from this we have that the line we are looking for must have a slope that is given by

k2=−1k1=−21

since the line y=2x+5 has a slope k1=2 (the coefficient in front of x).

The line we are looking for can thus be written in the form

y=−21x+m

with m as an unknown constant.

Because the point (2,4) should lie on the line, (2,4) must satisfy the equation of the line,

4=−212+m

i.e. m=5. The equation of the line is y=−21x+5.


Image:2_2_5d-2(2).gif
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