Question

50 pontos

de acordo com as equacoes parametricas {x=4t+2 y=3t+9}, informar a equacao segmentaria desta reta

Answer 1

Resposta:

$\text{Leia abaixo}$

Explicação passo-a-passo:

$\begin{cases}x = 4t + 2\\y = 3t + 9\end{cases}$

$\dfrac{x - 2}{4} = \dfrac{y - 9}{3}$

$3x - 6 = 4y - 36$

$3x - 4y = -30$

$\dfrac{3x}{30} - \dfrac{4y}{30} = \dfrac{-30}{30}$

$\boxed{\boxed{\dfrac{x}{10} - \dfrac{2y}{15} = -1}}$

Answer 2

Explicação passo-a-passo:

$\sf x=4t+2~\Rightarrow~4t=x-2~\Rightarrow~t=\dfrac{x-2}{4}~~(i)$

$\sf y=3t+9~\Rightarrow~3t=y-9~\Rightarrow~t=\dfrac{y-9}{3}~~(ii)$

Igualando (i) e (ii):

$\sf \dfrac{x-2}{4}=\dfrac{y-9}{3}$

$\sf 3\cdot(x-2)=4\cdot(y-9)$

$\sf 3x-6=4y-36$

$\sf 3x-4y=-36+6$

$\sf 3x-4y=-30$

$\sf \dfrac{3x}{-30}-\dfrac{4y}{-30}=\dfrac{-30}{-30}$

$\sf \red{\dfrac{-x}{10}+\dfrac{2y}{15}=1}$