write an equation of a line that is perpendicular to the given line and that passes through the given point (4,-6); m=3/5

Question

write an equation of a line that is perpendicular to the given line and that passes through the given point (4,-6); m=3/5

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Alexandra 31 mins 2021-09-15T23:05:09+00:00 1 Answer 0

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    2021-09-15T23:06:41+00:00

    Answer:

    y=-\frac{5}{3} x-\frac{42}{5}

    Step-by-step explanation:

    Given the slope and another point, simply plug them into the point-slope formula to find your y-intercept.

    y-y1=m(x-x1)\\y-(-6)=\frac{3}{5} (x-4)\\y+6=\frac{3}{5} x-\frac{12}{5} \\y=\frac{3}{5} x-\frac{42}{5}

    Now that we’ve found your y-intercept, we have the original equation. To find the perpendicular equation, you need the opposite reciprocal of your slope.

    To find the ‘opposite,’ change your slope’s sign. Since your slope is positive \frac{3}{5}, the opposite is -\frac{3}{5}.

    To find the ‘reciprocal,’ flip your fraction. This will make your slope -\frac{5}{3}.

    Your final equation is:

    y=-\frac{5}{3} x-\frac{42}{5}

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