Question

given the inequality $2x - 3y < 6$, convert to equation and find the $x$ and $y$ intercept points.
$(0,-2), (3,0)$
$(-2,0), (0,3)$
$(0,-2), (6,0)$
$(2,0), (0,-3)$

Explanation:

Step1: Convert inequality to equation

To find the intercepts, we first convert the inequality \(2x - 3y<6\) to the equation \(2x - 3y = 6\).

Step2: Find x - intercept

The x - intercept is the point where \(y = 0\). Substitute \(y = 0\) into the equation \(2x-3y = 6\):

$$
LATEXBLOCK0
$$

So the x - intercept is \((3,0)\).

Step3: Find y - intercept

The y - intercept is the point where \(x = 0\). Substitute \(x = 0\) into the equation \(2x - 3y=6\):

$$
LATEXBLOCK1
$$

So the y - intercept is \((0,-2)\).

Answer:

\((0, - 2),(3,0)\)