Question 4: A straight line passes through \( (5,2) \) and has a gradient of -2 . The equation of the line is:

To find the equation of the line that passes through the point \( (5,2) \) with a gradient (slope) of -2, we can use the point-slope form of a line's equation, which is expressed as \( y - y_1 = m(x - x_1) \). Here, \( m \) is the gradient, and \( (x_1, y_1) \) is the point on the line. Plugging in the values, we get: \[ y - 2 = -2(x - 5) \] Simplifying this yields: \[ y - 2 = -2x + 10 \] So, the final equation is: \[ y = -2x + 12 \] Lines with a negative slope, like this one, create a visual representation of balance on a scale—one side goes down as the other goes up! It’s a classic feature in linear equations that shows how one variable (y) changes in reaction to another (x). Understanding how lines behave has real-world applications in fields like economics, where you can model how one variable affects another—like price versus demand—helping businesses make crucial decisions. Visualizing this interaction can translate heavy data into actionable insights, making it a power play for strategists!