44.9k views
2 votes
Are the following equations parallel, perpendicular or neither?y = -1/2x + 310x - 5y = 15A. ParallelB. PerpendicularC. Neither

1 Answer

4 votes

By definition you know that the parallel lines have the same slope and that the slopes of the perpendicular lines satisfy the equation


\begin{gathered} m_2=(-1)/(m_1) \\ \text{ Where }m_1\text{ and }m_2\text{ are the slopes of lines 1 and 2, respectively} \end{gathered}

So, you can take the equation of the second line to the form


\begin{gathered} y=mx+b \\ \text{ Where} \\ m\text{ is slope of the line} \\ b\text{ is y-intercept} \end{gathered}

Then you have


\begin{gathered} 10x-5y=15 \\ \text{ Subtract 10x from both sides of the equation} \\ 10x-5y-10x=15-10x \\ -5y=15-10x \\ \text{ Divide by -5 on both sides of the equation} \\ (-5y)/(-5)=(15)/(-5)-(10x)/(-5) \\ y=-3+2x \\ y=2x-3 \end{gathered}

Now you know that the slope of the first line is -1/2 and the slope of the second line is 2, that is


\begin{gathered} m_1=-(1)/(2) \\ m_2=2 \end{gathered}

Let is see if the lines are perpendicular


\begin{gathered} m_2=(-1)/(m_1) \\ 2=((-1)/(1))/((-1)/(2)) \\ 2=(-1\cdot2)/(1\cdot-1) \\ 2=(2)/(1) \\ 2=2 \end{gathered}

Since we arrive at a true statement, then the lines are perpendicular.

Therefore, the correct answer is B. Perpendicular.

User Ali Nasserzadeh
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories