Which of the following is an equation of the line on the xy-plane that passes through the point (2,-1)and is parallel to the line with the equation 2x-3y=5?

Respuesta :

First we need to isolate y of the equation given

[tex]\begin{gathered} 2x-3y=5 \\ -3y=-2x+5 \\ y=\frac{2}{3}x-\frac{5}{3} \end{gathered}[/tex]

in order to be parallel lines, they have to have the same slope

The slope of the given line is 2/3

The equation will be

[tex]y+1=\frac{2}{3}(x-2)[/tex]

And then we isolate the y

[tex]\begin{gathered} y=\frac{2}{3}x-\frac{2}{3}-1 \\ y=\frac{2}{3}x-\frac{7}{3} \end{gathered}[/tex]

ANSWER

y=2/3 x -7/3