Question

State whether the given set of lines are parallel, perpendicular or neither.3x – 2y = 56y – 9x = 6The lines are perpendicular

Answer 1

Step-by-step explanation

Firstly, we must solve both equations for y:

Equation 1)

`\begin{gathered} 3x-2y=5, \\ 3x-2y+(2y-5)=5+(2y-5),\leftarrow\text{ additive property of equality} \\ 3x-5=2y, \\ 2y=3x-5, \\ (1)/(2)\cdot2y=(1)/(2)\cdot(3x-5),\leftarrow\text{ multiplicative property of equality} \\ y=(3x)/(2)-(5)/(2), \\ y={\textcolor{red}{(3)/(2)}}x-(5)/(2)\text{.} \end{gathered}`

Equation 2)

`\begin{gathered} 6y-9x=6, \\ 6y=9x+6, \\ y=(9x+6)/(6), \\ y=(9x)/(6)+(6)/(6), \\ y=(9)/(6)x+1, \\ y={\textcolor{red}{(3)/(2)}}x+1.{} \end{gathered}`

The value accompanying the variable x (after solving the equation for y!) is called the slope of the line ( in our equations, I've highlighted the slope with red color).

We say that two lines are parallel if their slopes are the same. That's what happens here.

Answer

The given set of lines are parallel.