Find the equation of the straight line with positive gradient and inclined at an angle of 45° to the line 3y-x+1=0 and passing through the point (2,0)?
2 Answers
is the equation of the straight line expected
Explanation:
Slope of the straight line,
is given by
The given line is
Rearranging in the standard form,
or
Comparing
Thus,
The slope of the new line is
Here, the angle of inclination is
Since the new line is having the positive slope with the straight line, the effective slope becomes combination of the straight line and the new line in the form given by
Substituting for
we have
The new line passes through the point,
Equation of a straight line passing through the point
Here;
Thus,
Simplifying
Cross multiplyng
Rearranging in the standard form,
we have
is the equation of the straight line expected
Explanation:
Note that the given line has slope
Let the reqd. line have slope
Given that, the angle between these two lines is
Thus, the reqd. line has slope