Question

Find the equation of the line which makes an angle of 120° with the x-axis and makes and intercept of -2 units on the y-axis.​

Answer 1

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

Given that,

• A line which makes an angle of 120° with the x-axis.

So, slope of line, m is given by

$\rm :\longmapsto\:m = tan120 \degree$

$\rm :\longmapsto\:m = tan(90 \degree + 30\degree)$

$\rm :\longmapsto\:m \: = - \: cot30\degree$

$\bf\implies \:m \: = - \: \sqrt{3}$

Also, given that line makes an intercept of - 2 units on y axis.

So,

$\bf\implies \:c = - 2$

We know,

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

So, on substituting the values, we get

$\rm :\longmapsto\:y = - \sqrt{3}x - 2$

$\bf\implies \:\boxed{\tt{ \: \: \: \: \sqrt{3}x + y + 2 = 0 \: \: \: \: }}$

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Additional Information :-

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.