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

Sagot :

Eunice1234idn

Answer: Perpendicular

Step-by-step explanation:

Convert both equations into slope-intercept form

[tex]y=-3x+4[/tex] ⇒ [tex]y=-3x+4[/tex]

[tex]x-3y=15[/tex] ⇒ [tex]y=\frac{1}{3} x-5[/tex]

Determine the slope of each equation

[tex]y=-3x+4[/tex]: SLOPE = -3

[tex]y=\frac{1}{3} x-5[/tex]: 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

[tex]-3\neq \frac{1}{3}[/tex]

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.

[tex](-3)*(\frac{1}{3} )=-1[/tex]

Hope this helps!! :)

Please let me know if you have any questions

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