Answer:
[tex]y = -x[/tex]
Step-by-step explanation:
Given
Perpendicular to: y - x = 7
Passes through: (2,2)
Required: The line equation
In [tex]y - x = 7[/tex]
[tex]y = x + 7[/tex]
An equation has the form: [tex]y = mx + b[/tex] where m is the slope
So:
[tex]m = 1[/tex]
The required equation is parallel to [tex]y = mx + b[/tex]. This means that:
[tex]m_2 = -\frac{1}{m_1}[/tex]
[tex]m_2 = -\frac{1}{1}[/tex]
[tex]m_2 = -1[/tex]
The equation isthen calculated using:
[tex]y = m(x - x_1) + y_2[/tex]
[tex]y = -1(x - (-2)) -(-2)[/tex]
[tex]y = -1(x +2) +2[/tex]
[tex]y = -x -2 +2[/tex]
[tex]y = -x[/tex]
