The length of the portion of the straight line `8x + 15 y = 120` intercepted between the axes is

Options

A. 14 units
B. 15 units
C. 16 units
D. 17 units

Answer

To find the length of the portion of the straight line \(8x + 15y = 120\) intercepted between the axes, we will follow these steps:

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

\[ 8x + 15(0) = 120 \implies 8x = 120 \implies x = \frac{120}{8} = 15 \]

So, the x-intercept is at the point \((15, 0)\).

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

\[ 8(0) + 15y = 120 \implies 15y = 120 \implies y = \frac{120}{15} = 8 \]

Thus, the y-intercept is at the point \((0, 8)\).

### Step 3: Determine the length of the line segment between the intercepts
Now, we need to find the length of the line segment connecting the points \((15, 0)\) and \((0, 8)\). We can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting the coordinates of the intercepts:

\[ \text{Distance} = \sqrt{(0 - 15)^2 + (8 - 0)^2} = \sqrt{(-15)^2 + 8^2} = \sqrt{225 + 64} = \sqrt{289} \]

### Step 4: Simplify the square root
Now, we simplify \(\sqrt{289}\):

\[ \sqrt{289} = 17 \]

Thus, the length of the portion of the straight line intercepted between the axes is \(17\) units.

### Final Answer
The length of the portion of the straight line \(8x + 15y = 120\) intercepted between the axes is \(17\) units.

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