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Determine the equation of the line that passes through the point (1/8,2) and is perpendicular to the line 5y+2x=2.

Sagot :

Step 1

Given;

Determine the equation of the line that passes through the point (1/8,2) and is perpendicular to the line 5y+2x=2.

Step 2

Find the slope of the new line based on a perpendicular relationship

[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \end{gathered}[/tex][tex]\begin{gathered} 5y=2-2x \\ y=\frac{2-2x}{5} \\ y=\frac{2}{5}-\frac{2}{5}x \\ -\frac{2}{5}=-\frac{1}{m_2} \\ 2m_2=5 \\ m_2=\frac{5}{2} \end{gathered}[/tex]

Thus the equation will be;

[tex]\begin{gathered} (\frac{1}{8},2) \\ y=\frac{5}{2}x+b \\ b=y-intercept \\ 2=\frac{5}{2}(\frac{1}{8})+b \\ 2=\frac{5}{16}+b \\ b=2-\frac{5}{16} \\ b=\frac{27}{16} \end{gathered}[/tex][tex]y=\frac{5}{2}x+\frac{27}{16}[/tex]

Answer;

[tex]y=\frac{5}{2}x+\frac{27}{16}[/tex]

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