Equation of a line which makes intercepts 3 and 4 on x axis and y axis respectively is

Options

A. 4 x + 3y = 12
B. 3x + 4y = 12
C. 6 x + y = 12
D. 4x - 3y = 12

Answer

To find the equation of a line that makes intercepts of 3 on the x-axis and 4 on the y-axis, we can follow these steps:

### Step 1: Identify the intercepts
The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0. Given that the x-intercept is 3, the coordinates of this point (let's call it A) are (3, 0).

The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0. Given that the y-intercept is 4, the coordinates of this point (let's call it B) are (0, 4).

### Step 2: Use the two-point form of the equation of a line
The two-point form of the equation of a line through two points (x1, y1) and (x2, y2) is given by:

\[ y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} (x - x_1) \]

In our case, we have:
- Point A (3, 0) → (x1, y1)
- Point B (0, 4) → (x2, y2)

### Step 3: Substitute the coordinates into the formula
Substituting the coordinates into the formula, we have:

\[ y - 0 = \frac{4 - 0}{0 - 3} (x - 3) \]

This simplifies to:

\[ y = \frac{4}{-3} (x - 3) \]

### Step 4: Simplify the equation
Now, we can simplify the equation:

\[ y = -\frac{4}{3} (x - 3) \]
\[ y = -\frac{4}{3}x + 4 \]

### Step 5: Rearrange to standard form
To convert this into standard form (Ax + By = C), we can multiply through by 3 to eliminate the fraction:

\[ 3y = -4x + 12 \]

Now, rearranging gives:

\[ 4x + 3y = 12 \]

### Final Answer
The equation of the line that makes intercepts of 3 on the x-axis and 4 on the y-axis is:

\[ 4x + 3y = 12 \]