Determine whether the are perpendicular. y=- 2 5 x+5;y= 5 2 x-8 (select )the lines (select )perpendicular .

Answer 1

Not quite sure of your line equations, but I hope this is what you intended:

y = -25x + 5

y = 52x - 8

For line questions usually the slope intercept form is useful, this is y = mx + b where m = gradient, and b = y intercept.

Often we need to rearrange equation to get this form, but for these equations we are already good to go.

First question: what is gradient of both lines? m = -25 and m = 52

Property of perpendicular lines: m1 x m2 = -1 (or "one is the negative reciprocal of the other").

-25 x 52 = -big number, so they are NOT perpendicular.

But maybe you meant these equations:

y = -²/₅x + 5

y = ⁵/₂x - 8

Also in slope intercept form, no rearrangement needed.

In this case, m1 = -²/₅ and m2 = ⁵/₂

m1 x m2 = -²/₅ x ⁵/₂ = -1 so these lines ARE perpendicular.