Question

1-Determine o coeficiente angular das retas que passam pelos pontos A e B nos seguintes casos:
A) A (-4 , 1) e B (2,3)
B) A(1/2,3/2) e B(1/4,5)

2- Calcule o coeficiente angular das seguintes retas : A ) 2x-y+1=0 B) x+2y=0
C) x/3+y/4=1 D ) y=-2/5x+1

Answer 1

Coeficiente angular A = ΔY/ΔX = $\frac{Y - Y_{0} }{X - X_{0}}$

A)
$\frac{3 - 1}{2 - (-4)} = \frac{2}{6} = \frac{1}{3}$

B)
$\frac{ \frac{1}{4} - \frac{1}{2} }{5 - \frac{3}{2}} = \frac{ \frac{1}{4} - \frac{2}{4} }{ \frac{10}{2} - \frac{3}{2}} = \frac{ -\frac{1}{4} }{\frac{7}{2}} = -\frac{1}{14}$

2 - 

equacao da reta generica e 
y = ax + b

a)
2x - y + 1 = 0
y = 2x + 1

coeficiente angular = 2

b)
x + 2y = 0
2y = -x
y = -x/2

coeficiente angular = -1/2

c) x/3 + y/4 = 1
y/4 = 1 - x/3
y = 4 - 4x/3

coeficiente agular = -4/3

d) y = -2/5x + 1

coeficiente angular = y = -(2/5).x  + 1

coeficiente angular = -2/5