Questions: Find the slope and reduce. P=(-4,2) Q=(4,-4) Slope =-[?]/square]

Find the slope and reduce. P=(-4,2) Q=(4,-4) Slope =-[?]/square]
Transcript text: Find the slope and reduce. \[ \begin{array}{c} P=(-4,2) \quad Q=(4,-4) \\ \text { Slope }=-\frac{[?]}{\square]} \end{array} \]
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Solution

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Solution Steps

Step 1: Define the Points

We are given two points: \[ P = (-4, 2) \quad \text{and} \quad Q = (4, -4) \]

Step 2: Calculate the Differences in Coordinates

Calculate the differences in the \( y \)-coordinates and \( x \)-coordinates: \[ \Delta y = y_2 - y_1 = -4 - 2 = -6 \] \[ \Delta x = x_2 - x_1 = 4 - (-4) = 4 + 4 = 8 \]

Step 3: Calculate the Slope

The slope \( m \) of the line passing through the points \( P \) and \( Q \) is given by: \[ m = \frac{\Delta y}{\Delta x} = \frac{-6}{8} = -0.75 \]

Final Answer

\[ \boxed{m = -\frac{3}{4}} \]

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