Question

Consider the equation −4x−y=3 A line parallel to the above line would have a slope of Correct A line perpendicular to the above line would have a slope of

Answer 1

Paralell: -4

Perpendicular: 1/4

Explanation:

We have the following equation:

`-4x-y=3`

Now, we have that an equation of a line in its slope-intercept form has the following form:

`\begin{gathered} y=mx+b \\ \text{where m is the slope and b is y-intercept} \end{gathered}`

We apply it in this case:

`\begin{gathered} -y=4x+3 \\ y=-4x-3 \\ \text{therefore} \\ m=-4 \end{gathered}`

When two lines are parallel, the slope is the same, while when they are perpendicular, the product of the slopes is equal to -1, we calculate each case below as follows:

`\begin{gathered} \text{ Parallel} \\ m_1=m_2 \\ m_2=-4 \\ \\ \text{ Perpendicular} \\ m_1\cdot m_2=-1 \\ m_2=(-1)/(m_1) \\ m_2=(-1)/(-4) \\ m_2=(1)/(4) \end{gathered}`