Please help me solve this equation!?

Write an equation of the line that passes through Point P and is perpendicular to the equation:

3x-5y=6

Point P= (-8,0)

I know how to solve the majority of these, but for some reason, this one is stumping me! Thank you!

1 Answer

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  • 7 years ago
    Favourite answer

    For perpendicular lines using standard form, switch the coefficients and change the middle sign:

    5x + 3y = ... then plug in the point's coordinates to see what it equals.

    5(-8) + 3(0) = -40

    So 5x + 3y = -40

    OR: get y by itself (slope-intercept form)

    3x = 6 + 5y

    3x - 6 = 5y

    3/5 x - 6/5 = y. This line has slope 3/5, and perpendicular lines have opposite reciprocal slopes, so your new line looks like y = -5/3 x + b. Plugging in (-8,0) you get

    0 = -5/3 (-8) + b

    0 = 40/3 + b

    -40/3 = b so the equation is y = -5/3 x - 40/3

    In standard form, multiply by 3: 3y = -5x - 40 then add 5x to both sides: 5x + 3y = -40

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