Questions: Find the slope of a line passing through the pair of points: (-3,4) and (2,-2)

Solution Steps

To find the slope of a line passing through two points, use the formula for the slope \( m \) which is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points. Substitute the given points into the formula to calculate the slope.

The two points given are \((-3, 4)\) and \((2, -2)\). We will denote these points as:

• \( (x_1, y_1) = (-3, 4) \)
• \( (x_2, y_2) = (2, -2) \)

The formula for the slope \( m \) of a line passing through two points is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the coordinates of the points into the slope formula: \[ m = \frac{-2 - 4}{2 - (-3)} = \frac{-6}{5} \]

The slope simplifies to: \[ m = -\frac{6}{5} \]

Final Answer