Question

Calcule o coeficiente angular das retas determinadas por:
a) A(3,4) B(6,7)
b) A(4,-4). B(-3,10)

Answer 1

Coeficiente angular da reta que passa pelos pontos $A(x_{_{A}},\,y_{_{A}})$ e $B(x_{_{B}},\,y_{_{B}}):$

$m=\dfrac{\Delta y}{\Delta x}\\\\\\ m=\dfrac{y_{_B}-y_{_A}}{x_{_B}-x_{_A}}~~~~~~(\text{com }x_{_B}\ne x_{_A})$

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a) $A(3,\,4)\text{ e }B(6,\,7):$

$m=\dfrac{7-4}{6-3}\\\\\\ m=\dfrac{3}{3}\\\\\\ \boxed{\begin{array}{c}m=1 \end{array}}$


b) $A(4,\,-4)\text{ e }B(-3,\,10):$

$m=\dfrac{10-(-4)}{-3-4}\\\\\\ m=\dfrac{10+4}{-7}\\\\\\ m=\dfrac{14}{-7}\\\\\\ \boxed{\begin{array}{c}m=-2 \end{array}}$


Bons estudos! :-)