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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)
Line 1: Line 1:
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Two straight lines are parallel if they have the same gradient. From the line
 +
<math>y=3x+1</math>, we can read off that it has a gradient of
 +
<math>3</math>
 +
(the coefficient in front of
 +
<math>x</math>
 +
), and hence the equation we are looking for has an equation of the form
 +
 +
 +
<math>y=3x+m</math>
 +
 +
 +
where
 +
<math>m</math>
 +
is a constant. The condition that the line should also contain the point
 +
<math>\left( -1 \right.,\left. 2 \right)</math>
 +
means that the point should satisfy the equation of the line
 +
 +
 +
<math>2=3\left( -1 \right)+m</math>
 +
 +
 +
which gives
 +
<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 y=3x+1, we can read off that it has a gradient of 3 (the coefficient in front of x ), and hence the equation we are looking for has an equation of the form


y=3x+m


where m is a constant. The condition that the line should also contain the point −12  means that the point should satisfy the equation of the line


2=3−1+m 


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


Image:S1_2_2_5_c.jpg

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