Question

A função de primeiro grau cujo gráfico passa pelos pontos A(−6,−27) e B(7,38) é dada por f(x)=ax+b.



Qual é o valor de a+b?

Answer 1

$\large\boxed{\begin{array}{l}\rm A(-6,-27)~~B(7,38)\\\rm a=\dfrac{y_B-y_A}{x_B-x_A}\\\\\rm a=\dfrac{38-[-27]}{7-[-6]}=\dfrac{38+27}{7+6}\\\\\rm a=\dfrac{65}{13}\\\\\rm a=5\\\rm f(x)=ax+b\\\rm f(7)=a\cdot 7+b\\\rm 38=5\cdot7+b\\\sf b+35=38\\\rm b=38-35\\\rm b=3\\\rm a+b=5+3\\\huge\boxed{\boxed{\boxed{\boxed{\rm a+b=8}}}}\end{array}}$