Answer: (A) y = x - 6
Explanation:
Since our line is perpendicular to the line y = -x + 5, then by definition, the gradients have a product of -1.
Since our equation is in the form, y = mx + b, we can just substitute, m = -1.
Thus, our gradient must be positive 1.
Now, we have a point it passes through so that coordinate must satisfy the line's equation. Let's use the point-gradient form, since we have a gradient and a point.
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y + 1 = 1(x - 5)[/tex]
[tex]y + 1 = x - 5[/tex]
[tex]y = x - 6[/tex] is our line that is perpendicular to [tex]y = -x + 5[/tex] and passes through the point [tex](5, -1)[/tex]
