Question

Reduce the equation into intercept form and find their intercept on the axis, 3x+2y-12=0

Answer 1

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

Given equation of line is

$\rm :\longmapsto\:3x + 2y - 12 = 0$

can be rewritten as

$\rm :\longmapsto\:3x + 2y = 12$

Now, divide both sides by 12, we get

$\rm :\longmapsto\:\dfrac{3x + 2y}{12} = \dfrac{12}{12}$

$\rm :\longmapsto\:\dfrac{3x}{12} + \dfrac{2y}{12} = 1$

$\rm :\longmapsto\:\dfrac{x}{4} + \dfrac{y}{6} = 1$

We know,

Equation of line which makes an intercept of a units and b units on x axis and y axis respectively, is

$\rm :\longmapsto\:\boxed{ \tt{ \: \frac{x}{a} + \frac{y}{b} = 1 \: }}$

So, on comparing, we get

↝ Intercept on x axis, a = 4

and

↝ Intercept on y axis, b = 6

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.