Check that the straight line through P1 and P2 goes through the origin.
P1(2∣4);P2(−1.5∣−3)
Für diese Aufgabe benötigst Du folgendes Grundwissen: Linear function
Insert the two points into the general line equation:
y=mx+t
1)2)4−3==2m+t−1.5m+t∣⋅(−1)
1)2)43==2m+t1.5m−t
Use the addition method.
Compute 1)+2).
7 = 3.5m :3.5 m = 3.57 m = 2 Plug m into one of the two functions.
4 = 2⋅2+t 4 = 4+t −4 t = 4−4 t = 0 y=2x
The line through P1 and P2 passes through the origin, since for x=0 the y-value is equal to 0.
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P1(−1∣3.5);P2(2∣−2)
Für diese Aufgabe benötigst Du folgendes Grundwissen: Linear function
Insert the two points into the general line equation:
y=mx+t
1)3.5=−1m+t2)−2=2m+t
For example, solve the linear system of equations with the addition method.
First multiply equation 1) on both sides by ∣⋅(−1)
1)−3.5=m−t2)−2=2m+t
Compute 1)+2)
−5.5 = 3m −211 = 3m :3 −2⋅311 = m −611 = m Plug m into one of the two equations.
−2 = 2⋅(−611)+t −2 = −311+t +311 −36+311 = t −35 = t Plug m and t into the general line equation.
m=−611;t=35
y=−611⋅x+35
The line through P1 and P2 does not pass through the origin, because for x=0 the y-value is equal to 35.
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