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Question

# Express the equation of the given line in standard form. Then find the distance from the given point $P\left(x_1, y_1\right)$ to that line. Round answers to the nearest hundredth.The line is perpendicular to the line $2 y=3 x-4$ and passes through the origin; $P(2,-5)$.

Solution

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Remember that the standard form of any linear equation is denoted by:

$Ax+By+C= \tag{1}0$

where $A \not = 0$ and $B \not = 0$.

Also, the distance from a point $P(x_1, y_1)$ to any nonvertical line is denoted by:

$d=\dfrac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2}} \tag{2}$

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