The equatio of the line whose slope is 3 and which cuts off an intercept 3 from the positive X-axis is

Options

A. `y=3x-9`
B. `y=3x+3`
C. `y=3x+9`
D. None of these

Answer

To find the equation of the line with a slope of 3 that cuts off an intercept of 3 from the positive X-axis, we can follow these steps:

### Step 1: Identify the intercept and slope
The slope (m) of the line is given as 3, and the x-intercept is given as 3. This means the line crosses the x-axis at the point (3, 0).

### Step 2: Use the point-slope form of the equation of a line
The point-slope form of the equation of a line is given by:
\[ y - y_1 = m(x - x_1) \]
where (x₁, y₁) is a point on the line and m is the slope.

### Step 3: Substitute the known values
Here, we have:
- Slope (m) = 3
- Point (x₁, y₁) = (3, 0)

Substituting these values into the point-slope form:
\[ y - 0 = 3(x - 3) \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ y = 3(x - 3) \]
\[ y = 3x - 9 \]

### Step 5: Write the final equation
The final equation of the line is:
\[ y = 3x - 9 \]

### Summary of the Solution
The equation of the line with a slope of 3 that cuts off an intercept of 3 from the positive X-axis is:
\[ y = 3x - 9 \]

---