Find the equation of the line, which makes intercepts -3 and 2 on the x- and y-axes respectively.

Step 1: Identify the intercepts

The problem states that the line makes an $x$ -intercept of $-3$ and a $y$ -intercept of $2$. We denote the $x$ -intercept as $a$ and the $y$ -intercept as $b$.

Step 2: Recall the intercept form of a line

The intercept form of the equation of a straight line is given by $\frac{x}{a} + \frac{y}{b} = 1$, where $a$ is the $x$ -intercept and $b$ is the $y$ -intercept.

Step 3: Substitute the intercept values

Now, substitute the given values of the $x$ -intercept ($a = -3$) and the $y$ -intercept ($b = 2$) into the intercept form equation.

Step 4: Simplify the equation

To simplify, find a common denominator for the fractions, which is $6$. Multiply the entire equation by $6$ to eliminate the denominators. Then, rearrange the terms to get the equation in the standard form $Ax + By + C = 0$.

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