Question

Wyznacz wzór funkcji liniowej wiedząc ,że należy do niej punkty:
a) A=(1,9) i B=(-2,-6) b) A=(1,5) i B=(-2,11) c) A=(-10,0) i B=(-6,7)

Answer 1

Odpowiedź:

Szczegółowe wyjaśnienie:

y=ax+b

a)

[tex]\left \{ {{9 = 1a + b} \atop {-6 = -2a + b}} \right. \\\\[/tex] / *(-1)

[tex]\left \{ {{9 = 1a + b} \atop {6 = 2a - b}} \right. \\\\[/tex]

9+6 = 1a + 2a +b - b

15 = 3a/:3

a = 5

9 = 5+b

b = 9-5 = 4

y=5x+4

b)

[tex]\left \{ {{5 = 1a + b} \atop {11 = -2a + b}} \right. \\\\[/tex]/*(-1)

[tex]\left \{ {{5 = 1a + b} \atop {-11 = 2a - b}} \right. \\\\[/tex]

5-11 = 1a + 2a +b - b

-5 = 3a /:3

a = - [tex]\frac{5}{3}[/tex]

5 = - [tex]\frac{5}{3}[/tex] + b

b = 5 + [tex]\frac{5}{3}[/tex] = 5 [tex]\frac{5}{3}[/tex] = 6 [tex]\frac{2}{3}[/tex]

y = [tex]-\frac{5}{3} x + 6\frac{2}{3}[/tex]

c)

[tex]\left \{ {{0 = -10a + b} \atop {7 = -6a + b}} \right. \\\\[/tex]/*(-1)

[tex]\left \{ {{0 = -10a + b} \atop {-7 = 6a - b}} \right. \\\\[/tex]

0-7=10a + 6a + b -b

-7  = 16a / :(16)

a = - [tex]\frac{7}{16}[/tex]

0 = -10 * (-[tex]\frac{7}{16}[/tex]) + b

0 = [tex]\frac{70}{16}[/tex] + b

b = [tex]\frac{70}{16}[/tex] = 4 [tex]\frac{6}{16}[/tex] = 4 [tex]\frac{3}{8}[/tex]

y = - [tex]\frac{7}{16}[/tex] + 4[tex]\frac{3}{8}[/tex]