Question

The point of intersection of 2x-3y=6,with coordinate axes are​

Answer 1

Intercept form

The straight line expressed in the form

$\quad\quad \frac{x}{a}+\frac{y}{b}=1$

intersects the x-axis at $(a,\:0)$ and the y-axis at $(0,\:b)$.

Solution:

The given straight line is

$\quad 2x-3y=6$

$\Rightarrow \frac{2x-3y}{6}=1$

$\Rightarrow \frac{2x}{6}-\frac{3y}{6}=1$

$\Rightarrow \frac{x}{3}+\frac{y}{-2}=1$

Thus the given straight line intersects the x-axis at $(3,\:0)$ and the y-axis at $(0,\:-2)$.

Remark: There can be another approach. Since we have to find point of intersection of the given line with the coordinate axes, put $y=0$ (intersection with the x-axis) and put $x=0$ (intersection with the y-axis).

$\quad$ When $x=0\Rightarrow y=-2$

$\quad$ When $y=0\Rightarrow x=3$

Thus the given straight line intersects the x-axis at $(3,\:0)$ and the y-axis at $(0,\:-2)$.

Answer 2

The complete question is,

The points of intersection of 2x - 3y = 6 with the coordinate axes are 1 point (3,0) & (0,4) (3,0) & (0,-2) (3,0) & (0,2) (5,0) & (0,-2)

Given:

The equation of line is 2x - 3y = 6

Options are (3,0) & (0,4) (3,0) & (0,-2) (3,0) & (0,2) (5,0) & (0,-2)

To find:

Find thee points of intersection.

Solution:

The given equation of line is 2x - 3y = 6.

Let us consider 2 conditions.

When x = 0, we get,

2 (0) - 3y = 6

- 3y = 6

y = -2

Therefore, the point of intersection is, (0, -2)

When y = 0, we get,

2x - 3 (0) = 6

2x = 6

x = 3

Therefore, the point of intersection is, (3, 0)

Hence (0,-2) (3,0) is the point of intersection of 2x-3y=6 with coordinate axes.