Answer:
[tex]y = -\frac{5}{2}(x - P) + Q[/tex]
Step-by-step explanation:
Required
Equation that goes through (P,Q) and is perpendicular to [tex]y = \frac{2}{5}x - 4[/tex]
The equation of a line is:
[tex]y = mx + c[/tex]
Where
[tex]m \to slope[/tex]
So by comparison:
[tex]y = \frac{2}{5}x - 4[/tex]
[tex]y = mx + c[/tex]
[tex]m = \frac{2}{5}[/tex]
The following relationship exists for perpendicular lines
[tex]m_2 = -\frac{1}{m}[/tex]
So, we have:
[tex]m_2 = -\frac{1}{2/5}[/tex]
This results to:
[tex]m_2 = -\frac{5}{2}[/tex] ---- This represents the slope of the new route
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
Where
[tex]m = -\frac{5}{2}[/tex] and
[tex](x_1,y_1) = (P,Q)[/tex]
This gives:
[tex]y = -\frac{5}{2}(x - P) + Q[/tex]
