Sum of the intercepts cut off by the line 2x + 3y = 6 on the axes is

Options

A. `(5)/(6)`
B. 6
C. 5
D. 1

Answer

To find the sum of the intercepts cut off by the line \(2x + 3y = 6\) on the axes, we can follow these steps:

### Step 1: Find the x-intercept
To find the x-intercept, we set \(y = 0\) in the equation of the line.

\[ 2x + 3(0) = 6 \]

This simplifies to:

\[ 2x = 6 \]

Now, solve for \(x\):

\[ x = \frac{6}{2} = 3 \]

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

### Step 2: Find the y-intercept
Next, we find the y-intercept by setting \(x = 0\) in the equation of the line.

\[ 2(0) + 3y = 6 \]

This simplifies to:

\[ 3y = 6 \]

Now, solve for \(y\):

\[ y = \frac{6}{3} = 2 \]

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

### Step 3: Calculate the sum of the intercepts
Now that we have both intercepts, we can find their sum:

\[ \text{Sum of intercepts} = \text{x-intercept} + \text{y-intercept} = 3 + 2 \]

Calculating this gives:

\[ 3 + 2 = 5 \]

### Final Answer
The sum of the intercepts cut off by the line on the axes is \(5\).

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