Question

The equation of a straight line which passes through the point $(-3,5)$ such that the portion of it between the axes is divided by the point in the ratio $5:3$ (reckoning from the x-axis) will be

• A. $x+y-2=0$
• B. $2x+y+1=0$
• C. $x+2y-7=0$
• D. $x-y+8=0$

Answer 1

The correct option is D

$x-y+8=0$

Find the equation of a straight line.

Equation of line passing through $(-3,5)$ is$y=mx+c$

$$\begin{gathered} \Rightarrow 5=-3+c \\ \Rightarrow c=8 \end{gathered}$$

Step 1: Find the coordinate of the point which passes through the given point.

Let the line meets the coordinate axis at $(a,0)$ and $(0,b).$

The point $(-3,5)$divides the line in the ratio$5:3.$

Using the section formula,

$-3=\frac{(5\times 0+3\times a)}{(5+3)}and5=\frac{(5\times b+3\times 0)}{(5+3)}$

$\Rightarrow a=-8andb=8$

Step 2: Find the slope of the given point.

The slope of the line joining the points $(-8,0)$ and $(0,8)=\frac{(y_2-y_1)}{(x_2-x_1)}$

$$\begin{gathered} =\frac{(0-8)}{(-8-0)} \\ =1 \\ \therefore m=1. \end{gathered}$$

Step 3: Find the equation of a straight line.

The required equation is $y=mx+c$

$$\begin{gathered} \Rightarrow y=x+8 \\ \Rightarrow x–y+8=0 \end{gathered}$$

Hence, option D is correct.