The general equation of a linear data is [tex]y = mx + c[/tex], where m is the slope, and c is the y intercept.
The equation of a line that passes through the origin and perpendicular to [tex]5x -2y = 8[/tex] is: [tex]y = -\frac{2}{5}x[/tex]
Given that:
[tex]5x -2y = 8[/tex]
Make 2y the subject
[tex]2y = 5x - 8[/tex]
Divide by 2 to make y the subject
[tex]y = \frac{5}{2}x -4[/tex]
The general form of a linear equation is:
[tex]y = mx + b[/tex]
By comparison:
[tex]m = \frac{5}{2}[/tex]
A line perpendicular to [tex]5x -2y = 8[/tex] will have the following slope (m2):
[tex]m_2 =-\frac{1}{m}[/tex]
Substitute [tex]m = \frac{5}{2}[/tex]
[tex]m_2 =-\frac{1}{5/2}[/tex]
[tex]m_2 =-\frac{2}{5}[/tex]
From the question, we understand that the line passes through (0,0) -- i.e. the origin.
This means that:
[tex](x_1,y_1) = (0,0)[/tex]
So, the equation is:
[tex]y = m_2(x - x_1) + y_1[/tex]
[tex]y = -\frac{2}{5}(x - 0) + 0[/tex]
[tex]y = -\frac{2}{5}(x) + 0[/tex]
[tex]y = -\frac{2}{5}x[/tex]
Hence, the equation of a line that passes through the origin and perpendicular to [tex]5x -2y = 8[/tex] is: [tex]y = -\frac{2}{5}x[/tex]
Read more about equation at:
https://brainly.com/question/11622505
