Final answer:
The slope of the line between points A (8, 9) and B (-2, 4) is calculated using the slope formula, which results in a value of 0.5. This means for every unit increase in the horizontal direction, the line rises by 0.5 units.
Step-by-step explanation:
To determine the slope of the line between two points A (8, 9) and B (-2, 4), we utilize the slope formula which is defined as the rise over the run, or the change in y over the change in x. This is represented in algebra as m = (y2 - y1) / (x2 - x1). In this formula, m stands for the slope, y2 and y1 are the y-coordinates of points B and A respectively, while x2 and x1 are the x-coordinates of points B and A respectively.
Applying the coordinates from points A and B to the formula, the slope calculation is as follows:
m = (4 - 9) / (-2 - 8) = (-5) / (-10) = 0.5
The slope of the line is 0.5, which means there is a rise of 0.5 on the vertical axis for every increase of 1 on the horizontal axis. This slope is constant for the entire length of a straight line, which determines its steepness and direction. The concept of the y-intercept is related but different; it represents the point at which the line crosses the vertical axis, but it is not needed for the calculation of the slope.