From Förberedande kurs i matematik 1

Revision as of 06:41, 21 August 2008 (edit) Tekbot (Talk | contribs) m (Robot: Automated text replacement (-[[Bild: +[[Image:)) ← Previous diff		Current revision (12:44, 24 September 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	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
-	<center> [[Image:2_2_5d-1(2).gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{Displayed math||<math>k_{2} = -\frac{1}{k_{1}} = -\frac{1}{2}</math>}}
-	{{NAVCONTENT_START}}	+
-	<center> [[Image:2_2_5d-2(2).gif]] </center>	+	since the line <math>y=2x+5</math> has a slope <math>k_{1}=2</math>
-	{{NAVCONTENT_STOP}}	+	(the coefficient in front of ''x'').
-	[[Image:2_2_5_d.jpg|center|300px]]	+
		+	The line we are looking for can thus be written in the form
		+
		+	{{Displayed math||<math>y=-\frac{1}{2}x+m</math>}}
		+
		+	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,
		+
		+	{{Displayed math||<math>4=-\frac{1}{2}\cdot 2+m\,,</math>}}
		+
		+	i.e. <math>m=5</math>. The equation of the line is <math>y=-\frac{1}{2}x+5</math>.
		+
		+
		+	<center>[[Image:2_2_5d-2(2).gif]]</center>

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Current revision

If two non-vertical lines are perpendicular to each other, their slopes \displaystyle k_{1} and \displaystyle k_{2} satisfy the relation \displaystyle k_{1}k_{2}=-1, and from this we have that the line we are looking for must have a slope that is given by

\displaystyle k_{2} = -\frac{1}{k_{1}} = -\frac{1}{2}

since the line \displaystyle y=2x+5 has a slope \displaystyle k_{1}=2 (the coefficient in front of x).

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

\displaystyle y=-\frac{1}{2}x+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,

\displaystyle 4=-\frac{1}{2}\cdot 2+m\,,

i.e. \displaystyle m=5. The equation of the line is \displaystyle y=-\frac{1}{2}x+5.