Question

Which equation represents a line which is perpendicular to the line y =- +522x - 5y = -302x + 5y = 152y-53 = 10O 5x + 2y 12

Answer 1

Answer:

The equation that represents the perpendicular line is;

$2y-5x=-10$

Explanation:

We want to find the equation of a line perpendicular to the line;

$y=-\frac{2}{5}x+5$

Recall that for two lines to be perpendicular to each other, their slope must be a negative reciprocal of one another.

$m_1.m_2=-1_{}_{}$

so;

$m_2=-\frac{1}{m_1}$

For the given equation, the slope of the given line is;

$m_1=-\frac{2}{5}$

To get the slope of the perpendicular line, let us substitute m1 to the equation above;

$\begin{gathered} m_2=-\frac{1}{m_1} \\ m_2=-\frac{1}{(-\frac{2}{5})_{}} \\ m_2=\frac{5}{2_{}} \end{gathered}$

So, the equation of the perpendicular line would be of the form;

$\begin{gathered} y=m_2x+c \\ y=\frac{5}{2}x+c \\ mu\text{ltiply through by 2} \\ 2y=5x+c \\ 2y-5x=c \end{gathered}$

The equation of the perpendicular line will be of the form;

$2y-5x=c$

Where c is a constant;

From the options, the only equation that is similar to the derived equation is;

$2y-5x=-10$

Therefore, the equation of the perpendicular line is;

$2y-5x=-10$