Final answer:
To find x so that the slope of the line through (-4, 3) and (x, -5) is -1, use the slope formula. The calculation shows that x = 4.
Step-by-step explanation:
To find the value of x for which the slope of the line through the points (-4, 3) and (x, -5) is -1, we can use the formula for the slope between two points, m = (y2 - y1) / (x2 - x1). We know that m = -1, y2 = -5, y1 = 3, x2 = x, and x1 = -4.
Applying the slope formula, we get -1 = (-5 - 3) / (x - (-4)). Simplifying the right side, we have -1 = -8 / (x + 4). To find x, we solve for x + 4 = 8. Therefore, x = 8 - 4, which gives us x = 4.