# 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**