What is the total length intercepted between both the axes by the line `8 x + 4y = 40 ? `

Options

A. 5
B. 10
C. 15
D. 20

Answer

To find the total length intercepted between both axes by the line given by the equation \(8x + 4y = 40\), we can follow these steps:

### Step 1: Rewrite the equation in intercept form
To find the intercepts, we can rewrite the equation in the intercept form, which is given by:

\[ \frac{x}{a} + \frac{y}{b} = 1 \]

where \(a\) is the x-intercept and \(b\) is the y-intercept.

### Step 2: Divide the entire equation by 40
We start with the equation:

\[ 8x + 4y = 40 \]

Now, divide every term by 40:

\[ \frac{8x}{40} + \frac{4y}{40} = \frac{40}{40} \]

### Step 3: Simplify the fractions
This simplifies to:

\[ \frac{x}{5} + \frac{y}{10} = 1 \]

### Step 4: Identify the intercepts
From the equation \(\frac{x}{5} + \frac{y}{10} = 1\), we can see that:

- The x-intercept \(a = 5\) (the point where the line intersects the x-axis)
- The y-intercept \(b = 10\) (the point where the line intersects the y-axis)

### Step 5: Calculate the total length intercepted
The total length intercepted between both axes is the sum of the x-intercept and the y-intercept:

\[ \text{Total Length} = a + b = 5 + 10 = 15 \]

### Final Answer
The total length intercepted between both the axes by the line \(8x + 4y = 40\) is **15**.

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