Question

Determine if the lines are parallel perpendicular or neither x-3y=15 and y=-3x+4

Answer 1

Answer: Perpendicular

Explanation:

Convert both equations into slope-intercept form

`y=-3x+4` ⇒
`y=-3x+4`

`x-3y=15` ⇒
`y=(1)/(3) x-5`

Determine the slope of each equation

`y=-3x+4`: SLOPE = -3

`y=(1)/(3) x-5`: SLOPE = 1/3

When two lines are parallel to each other, their slopes will be the same. However, since -3 does not equal 1/3, they are not parallel

`-3\\eq (1)/(3)`

When two lines are perpendicular to each other, the product of their slopes will be -1. Since -3 multiply by 1/3 is -1, they are perpendicular to each other.

`(-3)*((1)/(3) )=-1`

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