Question

4)determine, em cada caso, as coordenadas dos pontos em que a reta r intercepta os eixos coordenados.
A) 3x+2y-6=0
B)x+x+16=0
C)5x-4y+1=0​

Answer 1

$\large\boxed{\begin{array}{l}\tt a)~\sf 3x+2y-6=0\\\sf quando~x=0\\\sf 2y-6=0\\\sf 2y=6\\\sf y=\dfrac{6}{2}\\\sf y=3\\\sf quando~y=0\\\sf 3x-6=0\\\sf 3x=6\\\sf x=\dfrac{6}{3}\\\sf x=2\\\sf portanto~intercepta~\\\sf os~eixos~coordenados\\\sf em~A(2,0)~e~B(0,3)\end{array}}$

$\large\boxed{\begin{array}{l}\tt b)~\sf x+y+16=0\\\sf quando~x=0\\\sf y+16=0\\\sf y=-16\\\sf quando~y=0\\\sf x+16=0\\\sf x=-16\\\sf intercepta~os~eixos~coordenados\\\sf em~A(-16,0)~e~B(0,-16)\end{array}}$

$\large\boxed{\begin{array}{l}\tt c)~\sf 5x-4y+1=0\\\sf quando~x=0\\\sf -4y+1=0\\\sf 4y=1\\\sf y=\dfrac{1}{4}\\\sf quando~y=0\\\sf 5x+1=0\\\sf 5x=-1\\\sf x=-\dfrac{1}{5}\\\sf intercepta~os~eixos~coordenados~em\\\sf A\bigg(-\dfrac{1}{5}~,0\bigg)~e~B\bigg(0,\dfrac{1}{4}\bigg)\end{array}}$