Question

Y = 3/4x - 14, y = 4/3x + 12 Parallel Perpendicular Neither

Answer 1

We are given two line equations, we are asked to tell if they are parallel, perpendicular, or neither.

Two lines are parallel if they have the same slope. The slope of the line is the number that multiplies the variable "x" in the line equations, therefore, the slopes for each lines are:

`m_1=(3)/(4)`
`m_{2\text{ }}=(4)/(3)`

since the slopes are different, the lines are not parallel.

Two lines are perpendicular if the following relation between slopes is given

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

Apllying the previous formula for the slopes of the given lines

`m_1=-(1)/((4)/(3))=-(3)/(4)\\e m_2`

That means the lines are not perpendicular, therefore the answer is "neither"