Which choice is the equation of a line that passes through the point (5, –1) and is perpendicular to the line represented by this equation? y = −x + 5
a. y = x− 6
b. 5x − y = 5
c. y = −x− 1
d. 2x− 5y = −1

(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.





is our line that is perpendicular to and passes through the point

The correct answer would be the fourth choice