Answer:
[tex]y = -9/5x-4[/tex]
Step-by-step explanation:
Given
Passes through [tex](-5,5)[/tex]
Perpendicular to [tex]y = 5/9x - 4[/tex]
Required
The line equation
First, we calculate its slope (m)
In [tex]y = 5/9x - 4[/tex], the slope is:
[tex]m =5/9[/tex]
This is so because, the gradient intercept is:
[tex]y = mx + b[/tex]
By comparison, you have: [tex]m =5/9[/tex]
Since the required line and [tex]y = 5/9x - 4[/tex] are perpendicular, then the slope (m2) is:
[tex]m_2 = -1/m[/tex]
[tex]m_2 = -1/(5/9)[/tex]
[tex]m_2 = -9/5[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = -9/5(x - (-5)) + 5[/tex]
[tex]y = -9/5(x +5) + 5[/tex]
[tex]y = -9/5x-9 + 5[/tex]
[tex]y = -9/5x-4[/tex]
