Final answer:
The slope of the line through (2, 4) and (x, y) for y = x^2 - 2 is 2x - 4.
Step-by-step explanation:
The slope of a line can be found using the formula: m = (y2 - y1) / (x2 - x1). We can substitute the given coordinates (2, 4) and (x, y) into this formula. The equation for y is y = x^2 - 2, so we can plug in the x-coordinate from the second point to get the corresponding y-coordinate. Then we can substitute the coordinates into the slope formula and simplify to find the slope of the line between these two points.
The slope of the line through (2, 4) and (x, y) for y = x^2 - 2 is 2x - 4.