## Find the equation to the straight line cutting of an intercept unity from the positive direction of Y-axis and inclined at 45 degrees to the X axis:

### Solution:

Given that there is an intercept of unity, in the positive “Y”-axis direction.

Therefore the point on “Y” axis would be (0,1)

Since we have the point, all we need is the slope of the line to get the equation of the line.

We are also given that the line is inclined at 45 degrees to the “x” axis.

The slope of the line “m” is nothing but the , where is the angle made by the line with the “X”-axis.

Therefore the slope of the line would be tan (45)=1.

Since we have the slope as 1 and the point as (0,1), the point-slope form of the line is

(y-y1)=m(x-x1)

we have the point (x1,y1) as(0,1)

therefore the point-slope form of the line is

y-1=1(x-0)

y -1=x

**Therefore the desired line equation is y =x+1**