Find the equation of the st.line in each of the following problems :
Through the point `(-2,3)` with slope `-4`

Answer

To find the equation of the straight line that passes through the point (-2, 3) with a slope of -4, we can use the point-slope form of the equation of a line. The point-slope form is given by:

\[ y - y_1 = m(x - x_1) \]

Where:
- \((x_1, y_1)\) is a point on the line,
- \(m\) is the slope of the line.

### Step-by-Step Solution:

1. **Identify the given values:**
- The point \((x_1, y_1)\) is \((-2, 3)\).
- The slope \(m\) is \(-4\).

2. **Substitute the values into the point-slope form:**
\[ y - 3 = -4(x - (-2)) \]
This simplifies to:
\[ y - 3 = -4(x + 2) \]

3. **Distribute the slope on the right-hand side:**
\[ y - 3 = -4x - 8 \]

4. **Add 3 to both sides to isolate \(y\):**
\[ y = -4x - 8 + 3 \]
This simplifies to:
\[ y = -4x - 5 \]

5. **Rearranging into standard form (if needed):**
To express it in the standard form \(Ax + By + C = 0\):
\[ 4x + y + 5 = 0 \]

### Final Answer:
The equation of the straight line is:
\[ 4x + y + 5 = 0 \]