What is the equation of the line perpendicular to $y = - \frac{1}{16} x$ $y=-1/16x$ that passes through $(3, 4)$ $(3,4)$ ?

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What is the equation of the line perpendicular to $y = - \frac{1}{16} x$ $y=-1/16x$ that passes through $(3, 4)$ $(3,4)$ ?

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Answer 1 · 2016-02-16T03:53:51

Equation of desired line is $y = 16 x - 44$ $y=16x-44$

Explanation:

The equation of line $y = - (\frac{1}{16}) x$ $y=−(1/16)x$ is in slope-intercept form $y = m x + c$ $y=mx+c$ , where $m$ $m$ is slope and $c$ $c$ is intercept on $y$ $y$ axis.
Hence its slope is $- (\frac{1}{16})$ $−(1/16)$ .

As product of slopes of two perpendicular lines is $- 1$ $-1$ , slope of line perpendicular to $y = - (\frac{1}{16}) x$ $y=−(1/16)x$ is $16$ $16$ and slope-intercept form of the equation of line perpendicular will be $y = 16 x + c$ $y=16x+c$ .

As this line passes through (3,4), putting these as $(x, y)$ $(x, y)$ in $y = 16 x + c$ $y=16x+c$ , we get $4 = 16 \cdot 3 + c$ $4=16*3+c$ or $c = 4 - 48 = - 44$ $c=4-48=-44$ .

Hence equation of desired line is $y = 16 x - 44$ $y=16x-44$

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What is the equation of the line perpendicular to $y = - \frac{1}{16} x$ $y=-1/16x$ that passes through $(3, 4)$ $(3,4)$ ?

1 Answer

Explanation:

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