Question

Are the following lines parallel, perpendicular, or neither?

y= - 4/3x - 5 and y= 3/4x - 5
a) not enough information is given
b) neither
c) parallel
d) perpendicular

Answer 1

Perpendicular

Explanation:

Parallel lines mean lines that have same slope but since both equations have different slopes which you can check by looking at m-value in y = mx + b. In this case m1 or first slope is -4/3 and m2 or second slope is 3/4.

Perpendicular means that both lines are reciprocal to each other. This means the perpendicular condition is or satisfies
`\displaystyle \large{m_1m_2 = -1 \longrightarrow m_1 = -(1)/(m_2) \longrightarrow m_2 = -(1)/(m_1)}`

We have m1 = -4/3 and m2 = 3/4.

Therefore, -4/3 * 3/4 = -1 thus both lines are perpendicular to each other as it satisfies m1m2 = -1 condition.