The equation of the straight line through `(3,4)` and `(2,-1)` is ................

Answer

To find the equation of the straight line that passes through the points (3, 4) and (2, -1), we can use the point-slope form of the equation of a line. Here are the steps to derive the equation:

### Step 1: Identify the coordinates of the points
Let the points be:
- Point 1: \( (x_1, y_1) = (3, 4) \)
- Point 2: \( (x_2, y_2) = (2, -1) \)

### Step 2: Calculate the slope (m) of the line
The slope \( m \) of a line through two points is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the values:
\[ m = \frac{-1 - 4}{2 - 3} = \frac{-5}{-1} = 5 \]

### Step 3: Use the point-slope form of the line
The point-slope form of the equation of a line is:
\[ y - y_1 = m(x - x_1) \]
Using point \( (3, 4) \) and the slope \( m = 5 \):
\[ y - 4 = 5(x - 3) \]

### Step 4: Simplify the equation
Distributing the slope on the right side:
\[ y - 4 = 5x - 15 \]
Adding 4 to both sides:
\[ y = 5x - 15 + 4 \]
\[ y = 5x - 11 \]

### Final Equation
Thus, the equation of the straight line passing through the points (3, 4) and (2, -1) is:
\[ y = 5x - 11 \]