Question

Classify the following lines Y = 1 X – 2 3 & – 60 + 2y = 18 Intersecting, but not perpendicular Parallel Perpendicular The same line

Answer 1

7) We rearrange the second equation to compare it to the first one:

`\begin{gathered} -6x+2y=18 \\ 2y=6x+18 \\ y=3x+9 \end{gathered}`

The slopes are m1=1/3 and m2=3. They are not equal, nor negative reciprocals, so they are not parallel nor perpendicular. As they don't have the same slope, they will intersect.

Answer: Intersecting but not perpendicular.

8)

`\begin{gathered} 2x+3y=10 \\ 3y=-2x+10 \\ y=-(2)/(3)x+(10)/(3) \end{gathered}`
`\begin{gathered} -3x+2y=11 \\ 2y=3x+11 \\ y=(3)/(2)x+(11)/(2) \end{gathered}`

The slopes are negative reciprocals:

`m_1=-(1)/(m_2)`

As the slopes are negative reciprocals, both lines are perpendicular.

Answer: Perpendicular.