Find the equation of the line whose slope is -3 and x-intercept is also -3.

Answer

To find the equation of the line with a slope of -3 and an x-intercept of -3, we can follow these steps:

### Step 1: Identify the given information
- Slope (m) = -3
- x-intercept = -3

### Step 2: Determine the coordinates of the x-intercept
The x-intercept is the point where the line crosses the x-axis. At this point, the y-coordinate is 0. Therefore, the coordinates of the x-intercept are:
- Point P = (-3, 0)

### Step 3: 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 \((x_1, y_1)\) is a point on the line and \(m\) is the slope.

### Step 4: Substitute the values into the point-slope form
Here, we have:
- \(m = -3\)
- \(x_1 = -3\)
- \(y_1 = 0\)

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

### Step 5: Distribute and rearrange the equation
Now, distribute -3:
\[ y = -3x - 9 \]
To express this in standard form, we can rearrange it:
\[ 3x + y + 9 = 0 \]

### Final Equation
Thus, the equation of the line is:
\[ 3x + y + 9 = 0 \]