A line intersects the points \( (8,2) \) and \( (12,-10) \). hat is the slope of the line in simplest form? \( m=[?] \)

To find the slope \( m \) of the line that intersects the points \( (8, 2) \) and \( (12, -10) \), we use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates: \[ m = \frac{-10 - 2}{12 - 8} = \frac{-12}{4} = -3 \] So, the slope of the line in simplest form is \( m = -3 \). For a neat visual, imagine plotting these points on a graph. The line connecting them would be sloping downwards, reflecting the negative slope. You can picture it as a rollercoaster - zipping down from point \( (8, 2) \) to point \( (12, -10) \)! Now, think about real-world scenarios where slopes matter! Consider roads: a slope can affect drainage. If a road doesn’t have a negative slope (like this one), rainwater might pool instead of draining away. So, understanding slope isn't just math—it's practical for keeping roads safe and efficient!