Lösung 2.2:5c

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Two straight lines are parallel if they have the same gradient. From the line
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Two straight lines are parallel if they have the same slope. From the line
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<math>y=3x+1</math>, we can read off that it has a gradient of
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<math>y=3x+1</math>, we can read off that it has a slope of 3 (the coefficient in front of ''x''), and hence the equation we are looking for has an equation of the form
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<math>3</math>
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(the coefficient in front of
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<math>x</math>
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), and hence the equation we are looking for has an equation of the form
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{{Displayed math||<math>y=3x+m\,,</math>}}
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<math>y=3x+m</math>
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where ''m'' is a constant. The condition that the line should also contain the point (-1,2) means that the point should satisfy the equation of the line
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{{Displayed math||<math>2=3\cdot (-1)+m\,,</math>}}
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where
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which gives <math>m=5</math>. Hence, the equation of the line is <math>y=3x+5</math>.
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<math>m</math>
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is a constant. The condition that the line should also contain the point
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<math>\left( -1 \right.,\left. 2 \right)</math>
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means that the point should satisfy the equation of the line
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<math>2=3\left( -1 \right)+m</math>
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<center>[[Image:S1_2_2_5_c.jpg]]</center>
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which gives
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<math>m=5</math>. Hence, the equation of the line is
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<math>y=3x+5</math>.
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{{NAVCONTENT_START}}
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[[Image:S1_2_2_5_c.jpg]]
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<!--<center> [[Image:2_2_5c.png]] </center>-->
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{{NAVCONTENT_STOP}}
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Version vom 12:34, 24. Sep. 2008

Two straight lines are parallel if they have the same slope. From the line \displaystyle y=3x+1, we can read off that it has a slope of 3 (the coefficient in front of x), and hence the equation we are looking for has an equation of the form

Vorlage:Displayed math

where m is a constant. The condition that the line should also contain the point (-1,2) means that the point should satisfy the equation of the line

Vorlage:Displayed math

which gives \displaystyle m=5. Hence, the equation of the line is \displaystyle y=3x+5.


Image:S1_2_2_5_c.jpg
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_2.2:5c“