Question

seja r:3x-5y+2=0, encontre a reta S paralela à reta R e que passe pelo ponto A(-2;3). me ajudem por favor

Answer 1

$\Large\boxed{\begin{array}{l}\sf Considere~as~retas~a~seguir:\\\begin{cases}\sf r: y=m_1x+n_1\\\sf s: y=m_2x+n_2\end{cases}\\\sf r\parallel s\Longleftrightarrow m_1=m_2\\\sf ou~seja, duas~retas~s\tilde ao~paralelas\\\sf se~e~somente~se, seus~coeficientes\\\sf ~angulares~s\tilde ao~iguais.\end{array}}$

$\large\boxed{\begin{array}{l}\begin{cases}\sf r: 3x-5y+2=0\implies y=\dfrac{3}{5}x+\dfrac{2}{5}\\\sf s: y=m_sx+n\end{cases}\\\sf m_r=\dfrac{3}{5}\\\sf r\parallel s\Longleftrightarrow m_r=m_s\\\sf m_s=\dfrac{3}{5}\\\sf y=y_0+m\cdot (x-x_0)\\\sf y=3+\dfrac{3}{5}\cdot(x-(-2))\\\\\sf y=3+\dfrac{3}{5}(x+2)\\\\\sf y=3+\dfrac{3}{5}x+\dfrac{2}{5}\\\\\sf y=\dfrac{3}{5}x+\dfrac{17}{5}\end{array}}$