(Resolved)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:

Resolved Forum QuestionsCategory: Geometry(Resolved)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:
sakshi asked 1 month ago

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 \tan \left( \theta \right) , where \theta 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