Question

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?

Answer 1

First we need to isolate y of the equation given

`\begin{gathered} 2x-3y=5 \\ -3y=-2x+5 \\ y=(2)/(3)x-(5)/(3) \end{gathered}`

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

`y+1=(2)/(3)(x-2)`

And then we isolate the y

`\begin{gathered} y=(2)/(3)x-(2)/(3)-1 \\ y=(2)/(3)x-(7)/(3) \end{gathered}`

ANSWER

y=2/3 x -7/3