If a line intercepted between the coordinate axes is trisected at a point $A(4, 3)$ , which is nearer to $x$ -axis, then its equation is :

$\Rightarrow 4=\left(\frac{1\times0+2\times a}{1+2}\right)=\frac{2a}{3}$ $\Rightarrow a=6 \Rightarrow$ coordinate of $B$ is $B \left(6, 0\right)$ $3=\left(\frac{1\times a+2\times 0}{1+2}\right)=\frac{b}{3}$ $\Rightarrow b=9$ and $C\left(0, 9\right)$ Slope of line passing through $\left(6,0\right), \left(0,9\right)$ slope, $m=\frac{9}{-6}=-\frac{3}{2}$ Equation of line $y-0= \frac{-3}{2}\left(x- 6\right)$ $2y = -3x + 18$ $3x + 2y = 18$

If a line intercepted between the coordinate axes

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Straight lines

A straight line is a line having the shortest distance between two points.

A straight line can be represented as an equation in various forms, as show in the image below:

The following are the many forms of the equation of the line that are presented in straight line-

1. Slope – Point Form

Assume P0(x0, y0) is a fixed point on a non-vertical line L with m as its slope. If P (x, y) is an arbitrary point on L, then the point (x, y) lies on the line with slope m through the fixed point (x0, y0) if and only if its coordinates fulfil the equation below.

y – y₀ = m (x – x₀)

2. Two – Point Form

Let's look at the line. L crosses between two places. P₁(x₁, y₁) and P₂(x₂, y₂) are general points on L, while P (x, y) is a general point on L. As a result, the three points P₁, P₂, and P are collinear, and it becomes

The slope of P₂P = The slope of P₁P₂, i.e.

$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}$

Hence, the equation becomes:

y - y₁ =$ \frac{y_2-y_1}{x_2-x_1} (x-x1)$

3. Slope-Intercept Form

Assume that a line L with slope m intersects the y-axis at a distance c from the origin, and that the distance c is referred to as the line L's y-intercept. As a result, the coordinates of the spot on the y-axis where the line intersects are (0, c). As a result, the slope of the line L is m, and it passes through a fixed point (0, c). The equation of the line L thus obtained from the slope – point form is given by

y – c =m( x - 0 )

As a result, the point (x, y) on the line with slope m and y-intercept c lies on the line, if and only if

y = m x +c

If a line intercepted between the coordinate axes is trisected at a point $A(4, 3)$, which is nearer to $x$-axis, then its equation is :

The Correct Option is B

Solution and Explanation

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