1.

Find the angle described by the line x-y=0 to the x-axis

Answer»

Here X - y = 0 => x = y or y = x

=> if we draw a graph of y = x ---( i ), we get a straight LINE passing through the origin...

Now We also KNOW that , y = mx + c ----( ii )
where
m = slope of a line
c = y intercept ( where line CUTS y - axis )
if we compare the equation ( i ) and ( ii ) , we get
y = 1 × x + 0
y = m × x + c
m = 1 and c = 0
Here m = 1 , where m is a slope of a line
m = tan @
where @ = angle between the line and X-axis

=> tan @ = 1
=> tan @ = tan 45° ( since tan 45° = 1 )
=> @ = 45°

Thus angle betwenn the line ( i ) and X- axis is 45°


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