Solution 2.2:5c

From Förberedande kurs i matematik 1

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m (Lösning 2.2:5c moved to Solution 2.2:5c: Robot: moved page)
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Two straight lines are parallel if they have the same gradient. 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>3</math>
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(the coefficient in front of
 +
<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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 +
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<math>y=3x+m</math>
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 +
 +
where
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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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 +
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which gives
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<math>m=5</math>. Hence, the equation of the line is
 +
<math>y=3x+5</math>.
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[[Image:S1_2_2_5_c.jpg]]
[[Image:S1_2_2_5_c.jpg]]
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Revision as of 09:25, 18 September 2008

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


\displaystyle y=3x+m


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


\displaystyle 2=3\left( -1 \right)+m


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


Image:S1_2_2_5_c.jpg

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