Question

The line that is perpendicular to y=-x and passes through the point (2,4) is y=x+ ___?

A. -2
B. 2
C. -4
D. -1

*I'm confused about the answer because I think it should be 6 but that isn't an answer choice. ​

Answer 1

B. 2

Explanation:

We know when line 1 is perpendicular to line 2 so m1 × m2 = — 1

(m=slope)

so here we know that the slope of the new line is m2=1

and also line 2 cuts line 1 on a point such that (x,—x)

so we take a look at m2 and (x,—x) & (2,4) :

`we \: have \: \: m2 = 1 \\ so \\ m2 = ( - x - 4)/(x - 2) = 1 \\ \\ x = - 1 \\`

so (x,—x) will be ( —1,1)

now we know that line 2 passes through the point (—1,1)

now put the point as x & y :

`y = x + b \\ 1 = - 1 + b \\ b = 2`

so the final answer is 2