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Write the equation of the line that is perpendicular to the line 4y=5x−8 through the point (-5,4).A. y=−4/5xB. y=5/4xC. y=−5/4x−3D. y=4/5

Respuesta :

Given the line: 4y = 5x - 8

The slope of the given line = 5/4

The slope of the perpendicular line = -4/5

The line passes through the point (-5, 4 )

So, the point-slope equation will be:

[tex](y-4)=\frac{-4}{5}(x+5)[/tex]

Convert the equation to the slope-intercept form

So,

[tex]\begin{gathered} y-4=-\frac{4}{5}x-\frac{4}{5}\cdot5 \\ y-4=-\frac{4}{5}x-4 \\ y=-\frac{4}{5}x-4+4 \\ \\ y=-\frac{4}{5}x \end{gathered}[/tex]

So, the answer will be option A. y= −4/5 x

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