The general equation of a linear data is \(y = mx + c\), where m is the slope, and c is the y intercept.
The equation of a line that passes through the origin and perpendicular to \(5x -2y = 8\) is: \(y = -\frac{2}{5}x\)
Given that:
\(5x -2y = 8\)
Make 2y the subject
\(2y = 5x - 8\)
Divide by 2 to make y the subject
\(y = \frac{5}{2}x -4\)
The general form of a linear equation is:
\(y = mx + b\)
By comparison:
\(m = \frac{5}{2}\)
A line perpendicular to \(5x -2y = 8\) will have the following slope (m2):
\(m_2 =-\frac{1}{m}\)
Substitute \(m = \frac{5}{2}\)
\(m_2 =-\frac{1}{5/2}\)
\(m_2 =-\frac{2}{5}\)
From the question, we understand that the line passes through (0,0) -- i.e. the origin.
This means that:
\((x_1,y_1) = (0,0)\)
So, the equation is:
\(y = m_2(x - x_1) + y_1\)
\(y = -\frac{2}{5}(x - 0) + 0\)
\(y = -\frac{2}{5}(x) + 0\)
\(y = -\frac{2}{5}x\)
Hence, the equation of a line that passes through the origin and perpendicular to \(5x -2y = 8\) is: \(y = -\frac{2}{5}x\)
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