The equation of a straight line is represented as: [tex]y = mx + c[/tex]
The equation of the line is: [tex](c)\ y = -x +3[/tex]
The coordinates are given as:
[tex]M = (-5,5)[/tex]
[tex]N = (5,-2)[/tex]
[tex]O = (-8,2)[/tex]
First, we calculate the slope of line MO using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{2-5}{-8--5}[/tex]
[tex]m = \frac{-3}{-3}[/tex]
[tex]m = 1[/tex]
The line that passes through N is perpendicular to MO.
This means that, the slope (m2) of the line is:
[tex]m_2 = -\frac 1m[/tex]
So, we have:
[tex]m_2 = -\frac 1{1}[/tex]
[tex]m_2 = -1[/tex]
The equation of the line is then calculated as:
[tex]y = m_2(x - x_1) + y_1[/tex]
Where:
[tex]m_2 = -1[/tex]
[tex]N = (5,-2)[/tex] --- [tex](x_1,y_1)[/tex]
So, we have:
[tex]y = -1(x -5) - 2[/tex]
[tex]y = -x +5 - 2[/tex]
[tex]y = -x +3[/tex]
Hence, the equation of the line is: [tex](c)\ y = -x +3[/tex]
See attachment for the graph of the lines
Read more about equations of straight lines at:
https://brainly.com/question/21627259