Question

Equação da reta no caso abaixo:

Answer 1

Explicação passo-a-passo:

Essa reta passa pelos pontos A(-6, 3) e B(2, -7)

• Coeficiente angular:

$\sf m=\dfrac{y_B-y_A}{x_B-x_A}$

$\sf m=\dfrac{-7-3}{2-(-6)}$

$\sf m=\dfrac{-7-3}{2+6}$

$\sf m=\dfrac{-10}{8}$

$\sf m=\dfrac{-5}{4}$

• Equação da reta:

$\sf y-y_0=m\cdot(x-x_0)$

$\sf y-3=\dfrac{-5}{4}\cdot(x+6)$

$\sf 4\cdot(y-3)=-5\cdot(x+6)$

$\sf 4y-12=-5x-30$

$\sf 5x+4y-12+30=0$

$\sf \red{5x+4y+18=0}$ -> equação geral da reta

$\sf 4y=-5x-18$

$\sf y=\dfrac{-5x}{4}-\dfrac{18}{4}$

$\sf \red{y=\dfrac{-5x}{4}-\dfrac{9}{2}}$ -> equação reduzida da reta

Answer 2

a reta passa pelos pontos A(-6,3) e B(2,-7)

EGR:

$\begin{vmatrix}-6&3&1\\2&-7&1\\x&y&1\end{vmatrix}=0$

$\sf{-6(-7-y)-3(2-x)+1(2y+7x)=0}\\\sf{42+6y-6+3x+2y+7x=0}\\\sf{10x+8y+36=0\div2}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{5x+4y+18=0}}}}}$

ERR:

$\sf{5x+4y+18=0}\\\sf{4y=-5x-18}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{y=\dfrac{-5x-18}{4}}}}}}$

ESR:

$\sf{5x+4y+18=0\div-18}\\\sf{\dfrac{5x}{-18}+\dfrac{4y}{-18}+\dfrac{18}{-18}=0}\\\sf{-\dfrac{5x}{18}-\dfrac{2y}{9}-1=0}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{-\dfrac{5x}{18}-\dfrac{2y}{9}=1}}}}}$