Which equation is an equation of a line perpendicular to y = 5x + 7?

Answer 1

We need the slope intercept form of a line y = mx + b where m = gradient and b= y intercept.

The line given is y = 5x + 7 which is already in this form (otherwise we must rearrange).

So in this case, gradient is 5 (or 5 units up, and 1 unit across).

For parallel lines, the gradient is the same.

For perpendicular lines, then m1 x m2 = -1 (or each gradient is negative inverse of the other).

Hence, 5 x m2 = -1 => m2 = -¹/₅ (or slope goes down 1 unit, and across 5 units).

This gives us the general equation of family of parallel lines y = -¹/₅ x + n where n can be any number.

A specific example perpendicular line could be y = -¹/₅ x - 2.5