Write the standard form of the equation of the line passing through the point (1, 5) and perpendicular to the line 4x - 7y = – 28.

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03-11-2022
Mathematics

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Write the standard form of the equation of the line passing through the point (1, 5) and perpendicular to the line 4x - 7y = – 28.

Sagot :

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EvannyO735622 EvannyO735622 · Answer 1 · 2022-11-03T03:28:00-04:00

[tex]\begin{gathered} \text{The equation of line is,} \\ 4x-7y=-28 \\ 7y=4x+28 \\ y=\frac{4}{7}x+4 \\ \text{The slope is }\Rightarrow m=\frac{4}{7} \\ \text{The perpendicular slope}\Rightarrow m^{\prime}=-\frac{7}{4} \\ The\text{ equation passing through (1,5)} \\ y-y_1=m^{\prime}(x-x_1) \\ y-5=-\frac{7}{4}(x-1) \\ 4y-20=-7x+7 \\ 4y=-7x+27 \\ y=-\frac{7}{4}x+\frac{27}{4}(\text{Ans)} \end{gathered}[/tex]

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