Question

O grafico da função f(x)=mx + n passa pelos pontos A(1,-2) e B(4,2).Podemos então afirmar que:

a) m-n=-2
b)m+n=-2
c)m=¾
d)n=5/2
e)m.n=-1

Answer 1

f(1) = -2 => m + n = -2 => m = -2 - n
f(4) = 2 => 4.m + n = 2

Substituindo-se m = -2 - n em 4.m + n = 2, temos:

4.(-2 - n) + n = 2
-8 - 4.n + n = 2
-3.n = 10
n = -10/3

m = -2 - n => m = -2 + 10/3 => m = -12/6 + 20/6 = 8/6 = 4/3

Answer 2

$\left\{{{f(1)=-2}\atop{f(4)=2}}\right\rightarrow\left\{{{-2=m(1)+n}\atop{2=m(4)+n}}\right\to\left\{{{m+n=-2}\atop{n=2-4m}}\right\to\left\{{{m+(2-4m)=-2}\atop{n=2-4m}}\right\\\\\left\{{{m=\frac{4}{3}}\atop{n=2-4\cdot(\frac{4}{3})}}\right\left\{{{m=\frac{4}{3}}\atop{n=-\frac{10}{3}}}\right\\\\\\\\m+n=\dfrac{4}{3}+\left(-\dfrac{10}{3}\right)\to\ m+n=-\dfrac{6}{3}\to\ \boxed{m+n=-2}\\\\Alternativa\ b)$