Question

escreva a equação da reta que passa pelos pontos A (0,2) e B (2,3)

Answer 1

=> Sem precisar de fómula, só aplicando os conceitos de função do 1º grau
y= ax + b
==========
a = 3- 2 / 2-0
a= 1/2
a = 0,5
============ acha b substituindo qualquer ponto
y = ax + b
2 = 0 + b
b= 2
============== pronto
y = 0,5x + 2 ou
y - 0,5x - 2 = 0

Answer 2

$A~(0~;~2)~~~e~~~B~(2~;~3)\\\\\\Calculando ~~o~~coeficiente~~angular:\\\\ m= \dfrac{y_b-y_a}{x_b-x_a} \to~~ m= \dfrac{3-2}{2-0} \to~~ \boxed{m= \dfrac{1}{2} } \\\\\\ (y-y_{\°})=m(x-x_{\°}) \\\\\\Usando ~~o~~ponto~~A~(0~;~2):\\\\ (y-2)= \dfrac{1}{2}(x-0) \to\\\\ y-2= \dfrac{x}{2} \to\\\\ \large\boxed{y-\dfrac{x}{2}-2=0 ~~\overrightarrow{~~~~~~} ~Geral }\\\\ \large\boxed{ y=\dfrac{x}{2}+2 ~~\overrightarrow{~~~~~~} ~Reduzida}$