Determine the value of “k” when the lines y=k3x+2 and y=14x+2 are perpendicular. Show your work. (3 marks/PS)

Question

Determine the value of “k” when the lines y=k3x+2 and y=14x+2 are perpendicular. Show your work. (3 marks/PS)

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Nguyệt Ánh 1 year 2021-09-04T10:58:02+00:00 1 Answers 1 views 0

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  1. Farah
    0
    2021-09-04T10:59:31+00:00
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    Answer:

    [tex]k=-\frac{1}{42}[/tex]

    Step-by-step explanation:

    Hi there!

    What we need to know:

    • Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)
    • Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2)

    Given the equation [tex]y=14x+2[/tex], we can identify the slope (m) to be 14. This means that the slope of a perpendicular line would have to be [tex]-\frac{1}{14}[/tex] since that is its negative reciprocal.

    In the equation [tex]y=k*3x+2[/tex], the slope would be 3k. 3k would be equal to [tex]-\frac{1}{14}[/tex]:

    [tex]3k=-\frac{1}{14}[/tex]

    Divide both sides by 3 to solve for k

    [tex]k=-\frac{1}{42}[/tex]

    I hope this helps!

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