Question

Find the equation of the lines which pass through the point (-2,5) and are equally inclined to the coordinate axes.

Answer 1

There are two lines possible passing through any point on coordinate plane which are equally inclined to the coordinate axes. 
The slopes of the lines are 1 and -1.

let the equation of the required line be y=mx+c

for slope(m) = 1,
so the equation becomes y=x+c

as it passes through (-2,5)
⇒ 5 = -2 + c
⇒ c = 5+2 = 7
So one of the equation is 
y = x+7

for slope(m) = -1,
so the equation becomes y=-x+c

as it passes through (-2,5)
⇒ 5 = -(-2) + c
⇒ 5 = 2 + c
⇒ c = 5-2 = 3
So other equation is 
y = -x+3