Question

Find the equation of the straight line cutting off y intercept 5 unit and making inclination 135degree

Answer 1

$\large\underline{\sf{Solution-}}$

Given that, line cutting off y - intercept 5 unit and making inclination 135 degree with positive direction of x axis measured in anti-clockwise direction.

Let us assume that l is the required line line cutting off y - intercept 5 unit and making inclination 135 degree with positive direction of x axis measured in anti-clockwise direction.

So,

Intercept on y - axis, c = 5

and

Slope of line l, m = tan135° = - 1.

We know, Intercept Form of a line : If a line makes an intercept of c units on y - axis and having slope m, then equation of line is y = mx + c.

So, Required equation of line is

$\rm :\longmapsto\:y = - 1 \times x + 5$

$\rm :\longmapsto\:y = - x + 5$

$\rm \implies\:\boxed{ \tt{ \: x + y = 5 \: }}$

More to Know :-

Different forms of equations of a straight line

1. Equations of horizontal and vertical lines

Equation of line parallel to x - axis passes through the point (a, b) is x = a.

Equation of line parallel to x - axis passes through the point (a, b) is x = a.

2. Point-slope form equation of line

Equation of line passing through the point (a, b) having slope m is y - b = m(x - a)

3. Slope-intercept form equation of line

Equation of line which makes an intercept of c units on y axis and having slope m is y = mx + c.

4. Intercept Form of Line

Equation of line which makes an intercept of a and b units on x - axis and y - axis respectively is x/a + y/b = 1.

5. Normal form of Line

Equation of line which is at a distance of p units from the origin and perpendicular makes an angle β with the positive X-axis is x cosβ + y sinβ = p.