Question

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

Answer 1

Answer: (A) y = x - 6
Step-by-step 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.


`y - y_1 = m(x - x_1)`

`y + 1 = 1(x - 5)`

`y + 1 = x - 5`


`y = x - 6` is our line that is perpendicular to
`y = -x + 5` and passes through the point
`(5, -1)`