Question

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

Answer 1

Answer: Perpendicular

Step-by-step explanation:

Convert both equations into slope-intercept form

$y=-3x+4$ ⇒ $y=-3x+4$

$x-3y=15$ ⇒ $y=\frac{1}{3} x-5$

Determine the slope of each equation

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

$y=\frac{1}{3} x-5$: 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

$-3\neq \frac{1}{3}$

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.

$(-3)*(\frac{1}{3} )=-1$

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