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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

Respuesta :

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]

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