ANSWER
The required equation is
[tex]y = 5x + 1[/tex]
EXPLANATION
The given line passes through the point
[tex](5,0) \: and \: (0,1)[/tex]
The slope of this line is given by the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1} [/tex]
This implies that,
[tex]m = \frac{1 - 0}{0 - 5} [/tex]
[tex]m = - \frac{1}{5} [/tex]
The product of the slope of the two perpendicular lines should be negative one.
Thus,
[tex]m_1\times m_2=-1[/tex]
This implies that,
[tex] - \frac{1}{5} \times m_2=-1[/tex]
We multiply through by
[tex] - 5[/tex]
to obtain,
[tex] m_2=-1 \times - 5[/tex]
[tex] m_2=5[/tex]
Therefore the slope of the line perpendicular to the given line is
[tex]5.[/tex]
We use the slope intercept formula
[tex]y =m x + b[/tex]
where
[tex]b = 1[/tex]
is the y-value of the y-intercept.
We therefore have,
[tex]y = 5x + 1[/tex]
as the required equation.
The correct answer is C.
