Final answer:
The slope for the points (2, 12) and (-2, 12) is 0, indicating a horizontal line. For the points (-3, -2) and (1, 4), the slope is 1.5, indicating that the line rises as x increases.
Step-by-step explanation:
To determine the slope of a line through two points, we use the formula m = (y2 - y1) / (x2 - x1), where m is the slope, (x1, y1) is the first point, and (x2, y2) is the second point. Let's calculate the slope for the two pairs of points given:
- For the points (2, 12) and (-2, 12), the slope m = (12 - 12) / (-2 - 2) = 0 / -4 = 0. So, the slope is 0, meaning the line is horizontal.
- For the points (-3, -2) and (1, 4), the slope m = (4 - (-2)) / (1 - (-3)) = 6 / 4 = 1.5. So, the slope is 1.5, which means for every 1 unit increase in x, y increases by 1.5 units.
The significance of the slope is that it indicates how steep the line is and in which direction it goes. A slope of 0 indicates a horizontal line, while a positive slope indicates the line rises as it moves from left to right.