Lösung 2.2:5c - Versionsgeschichte

Tek: Replaced figure with metapost figure

2009-08-18T11:34:22Z

Replaced figure with metapost figure

← Nächstältere Version		Version vom 11:34, 18. Aug. 2009
Zeile 10:		Zeile 10:


-	<center>~~[[Image~~:~~S1_2_2_5_c~~.~~jpg]]~~</center>	+	<center>{{:2.2.5c - Solution - The line y = 3x + 1 and the line y = 3x + 5 through the point (-1,2)}}</center>

Moni um 09:21, 9. Aug. 2009

2009-08-09T09:21:19Z

← Nächstältere Version		Version vom 09:21, 9. Aug. 2009
Zeile 1:		Zeile 1:
-	Zwei Geraden sind parallel, falls sie dieselbe Steigung haben. Wir sehen, dass die Gerade <math>y=3x+1</math> Steigung 3 hat, ~~und~~ also muss unsere Gerade die Gleichung	+	Zwei Geraden sind parallel, falls sie dieselbe Steigung haben. Wir sehen, dass die Gerade <math>y=3x+1</math> Steigung 3 hat, also muss unsere Gerade die Gleichung

	{{Abgesetzte Formel\|\|<math>y=3x+m\,,</math>}}		{{Abgesetzte Formel\|\|<math>y=3x+m\,,</math>}}

-	haben, wo wir ''m'' bestimmen müssen. Nachdem die Gerade durch den Punkt (-1,2) gehen soll, muss dieser Punkt die Gleichung der Gerade erfüllen.	+	haben, wobei wir ''m'' bestimmen müssen. Nachdem die Gerade durch den Punkt (-1,2) gehen soll, muss dieser Punkt die Gleichung der Gerade erfüllen.

	{{Abgesetzte Formel\|\|<math>2=3\cdot (-1)+m\,,</math>}}		{{Abgesetzte Formel\|\|<math>2=3\cdot (-1)+m\,,</math>}}

-	Dies ergibt <math>m=5</math>, ~~und~~ die Gleichung der Gerade ~~ist~~ daher <math>y=3x+5</math>.	+	Dies ergibt <math>m=5</math>, also ist die Gleichung der Gerade daher <math>y=3x+5</math>.


	<center>[[Image:S1_2_2_5_c.jpg]]</center>		<center>[[Image:S1_2_2_5_c.jpg]]</center>

Markus.bez: Sprache und Formulierung

2009-06-09T09:37:19Z

Sprache und Formulierung

← Nächstältere Version		Version vom 09:37, 9. Jun. 2009
Zeile 1:		Zeile 1:
-	Zwei Geraden sind parallel falls sie dieselbe Steigung haben. Wir sehen dass die ~~Steigung von der Geraden~~ <math>y=3x+1</math>, 3 ~~ist~~, und also muss unsere Gerade die Gleichung	+	Zwei Geraden sind parallel, falls sie dieselbe Steigung haben. Wir sehen, dass die Gerade <math>y=3x+1</math> Steigung 3 hat, und also muss unsere Gerade die Gleichung

	{{Abgesetzte Formel\|\|<math>y=3x+m\,,</math>}}		{{Abgesetzte Formel\|\|<math>y=3x+m\,,</math>}}

Martin um 17:38, 12. Mär. 2009

2009-03-12T17:38:04Z

← Nächstältere Version		Version vom 17:38, 12. Mär. 2009
Zeile 1:		Zeile 1:
-	~~Two straight lines are~~ parallel ~~if they have the same slope~~. ~~From the line~~	+	Zwei Geraden sind parallel falls sie dieselbe Steigung haben. Wir sehen dass die Steigung von der Geraden <math>y=3x+1</math>, 3 ist, und also muss unsere Gerade die Gleichung
-	<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~~	+

	{{Abgesetzte Formel\|\|<math>y=3x+m\,,</math>}}		{{Abgesetzte Formel\|\|<math>y=3x+m\,,</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~~	+	haben, wo wir ''m'' bestimmen müssen. Nachdem die Gerade durch den Punkt (-1,2) gehen soll, muss dieser Punkt die Gleichung der Gerade erfüllen.

	{{Abgesetzte Formel\|\|<math>2=3\cdot (-1)+m\,,</math>}}		{{Abgesetzte Formel\|\|<math>2=3\cdot (-1)+m\,,</math>}}

-	~~which gives~~ <math>m=5</math>~~. Hence~~, ~~the equation of the line is~~ <math>y=3x+5</math>.	+	Dies ergibt <math>m=5</math>, und die Gleichung der Gerade ist daher <math>y=3x+5</math>.


	<center>[[Image:S1_2_2_5_c.jpg]]</center>		<center>[[Image:S1_2_2_5_c.jpg]]</center>

Tekbot: hat „Solution 2.2:5c“ nach „Lösung 2.2:5c“ verschoben: Robot: moved page

2008-10-22T13:58:05Z

hat „Solution 2.2:5c“ nach „Lösung 2.2:5c“ verschoben: Robot: moved page

← Nächstältere Version

Version vom 13:58, 22. Okt. 2008

Tekbot: Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)

2008-10-22T08:28:48Z

Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)

← Nächstältere Version		Version vom 08:28, 22. Okt. 2008
Zeile 2:		Zeile 2:
	<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		<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

-	{{~~Displayed math~~\|\|<math>y=3x+m\,,</math>}}	+	{{Abgesetzte Formel\|\|<math>y=3x+m\,,</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		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

-	{{~~Displayed math~~\|\|<math>2=3\cdot (-1)+m\,,</math>}}	+	{{Abgesetzte Formel\|\|<math>2=3\cdot (-1)+m\,,</math>}}

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

Tek um 12:34, 24. Sep. 2008

2008-09-24T12:34:37Z

← Nächstältere Version		Version vom 12:34, 24. Sep. 2008
Zeile 1:		Zeile 1:
-	Two straight lines are parallel if they have the same ~~gradient~~. From the line	+	Two straight lines are parallel if they have the same slope. From the line
-	<math>y=3x+1</math>, we can read off that it has a ~~gradient~~ of	+	<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
-	~~<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	+

		+	{{Displayed math\|\|<math>y=3x+m\,,</math>}}

-	~~<math>y=3x+~~m~~</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

		+	{{Displayed math\|\|<math>2=3\cdot (-1)+m\,,</math>}}

-	~~where~~	+	which gives <math>m=5</math>. Hence, the equation of the line is <math>y=3x+5</math>.
-	<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>~~	+	<center>[[Image:S1_2_2_5_c.jpg]]</center>
-		+
-		+
-	~~which gives~~	+
-	~~<math>m=5</math>. Hence, the equation of the line is~~	+
-	~~<math>y=3x+5</math>.~~	+
-		+
-		+
-	~~{{NAVCONTENT_START}}~~	+
-	[[Image:S1_2_2_5_c.jpg]]	+
-	~~<!--<center> [[Image:2_2_5c.png~~]] </center>~~-->~~	+
-	~~{{NAVCONTENT_STOP}}~~	+

Ian um 09:25, 18. Sep. 2008

2008-09-18T09:25:06Z

← Nächstältere Version		Version vom 09:25, 18. Sep. 2008
Zeile 1:		Zeile 1:
		+	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>.
		+
		+
	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
	[[Image:S1_2_2_5_c.jpg]]		[[Image:S1_2_2_5_c.jpg]]
	<!--<center> [[Image:2_2_5c.png]] </center>-->		<!--<center> [[Image:2_2_5c.png]] </center>-->
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}

Tekbot: Lösning 2.2:5c moved to Solution 2.2:5c: Robot: moved page

2008-09-09T08:47:43Z

Lösning 2.2:5c moved to Solution 2.2:5c: Robot: moved page

← Nächstältere Version

Version vom 08:47, 9. Sep. 2008

Tekbot: Robot: Automated text replacement (-[[Bild: +[[Image:)

2008-08-21T06:40:59Z

Robot: Automated text replacement (-[[Bild: +[[Image:)

← Nächstältere Version		Version vom 06:40, 21. Aug. 2008
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	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
-	[[~~Bild~~:S1_2_2_5_c.jpg]]	+	[[Image:S1_2_2_5_c.jpg]]
-	<!--<center> [[~~Bild~~:2_2_5c.png]] </center>-->	+	<!--<center> [[Image:2_2_5c.png]] </center>-->
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}