Question

Which equation represents a line which is parallel to the line y= --2-5?O 23 + 3y = -9O 3y – 21 = -12O 31 + 2y = -2.31 – 2y = 12

Answer 1

Two lines are parallel if the have the same slop. The slope can be seen if you write the equation of the line in the form

`y=mx+b,`

in this case m is the slope. So, if you write the last equation, the one that is selected in this form, you have

`\begin{gathered} 3x-2y=12 \\ 2y=3x-12 \\ y=(3)/(2)x-6 \end{gathered}`

so the slope is 3/2 and it is different from the original one. On the other hand, if we analyze the third equation

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

we see that the slope of 3x+2y=-2 is the same that the slope of y=-3/2x-5, so they are parallel.