Find the equation of the line whose slope is `- 4/3` and which passes through `(-3, 4)`.

Answer

To find the equation of the line with a slope of \(-\frac{4}{3}\) that passes through the point \((-3, 4)\), we can use the point-slope form of the equation of a line, which is given by:

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

Where:
- \(m\) is the slope of the line,
- \((x_1, y_1)\) is the point through which the line passes.

### Step 1: Identify the slope and the point
Given:
- Slope \(m = -\frac{4}{3}\)
- Point \((x_1, y_1) = (-3, 4)\)

### Step 2: Substitute the values into the point-slope formula
Substituting \(m\), \(x_1\), and \(y_1\) into the point-slope form:

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

This simplifies to:

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

### Step 3: Distribute the slope on the right side
Now, distribute \(-\frac{4}{3}\):

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

Calculating \(-\frac{4}{3} \cdot 3\):

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

### Step 4: Add 4 to both sides
Now, add 4 to both sides to isolate \(y\):

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

This simplifies to:

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

### Step 5: Rearranging to standard form
To express the equation in standard form \(Ax + By + C = 0\):

\[ \frac{4}{3}x + y = 0 \]

Multiplying through by 3 to eliminate the fraction:

\[ 4x + 3y = 0 \]

### Final Equation
Thus, the equation of the line is:

\[ 4x + 3y = 0 \]