Question

7) Qual a expressão da função definida pelo gráfico. *
3 pontos
Imagem sem legenda
f(x) = x + ½
f(x) = x - ½
f(x) = ½ x - 1
f(x) = ½ x + 1
f(x) = 2x + 1

Answer 1

Equação de uma reta passando pelos pontos $(\text x_1,\text y_1) \ \text e \ (\text x_2,\text y_2)$

$\displaystyle \text y -\text y_{1,2}=\text m(\text x-\text x_{1,2}) \\\\\\ {\text{onde}}:\\\\ \text x_{1,2} \ , \ \text y_{1,2} = \text{ponto 1 ou o ponto 2} \\\\ \text m =\frac{\text y_2-\text y_1}{\text x_2-\text x_1}$

Queremos a equação da reta que passa pelos pontos (0,1) e (2,2).

$\displaystyle \text{coeficiente angular ( m )}: \\\\\ \text m =\frac{2-1}{2-0} \to \boxed{\ \text m = \frac{1}{2}\ } \\\\\\ \underline{\text{equa{\c c}{\~a}o da reta}}\\\\\ \text y-\text y_{1,2}=\text m(\text x-\text x_{1,2})\\\\ \underline{\text{substituindo o ponto (0,1)}}: \\\\ \text y - 1 = \frac{1}{2}(\text x-0) \\\\\\ \huge\boxed{\ \text y = \frac{1}{2}\text x+ 1\ }\checkmark$