Final answer:
The points (-7,8) and (-7,0) indicate a vertical line with an undefined or infinite slope, not positive or negative. For the points (1, 0.1) and (7, 26.8), the slope is 4.45, which is positive. The appearance of slopes is upward to the right for positive, downward to the right for negative, and horizontal for zero slope.
Step-by-step explanation:
The slope of a line passing through two points (x1, y1) and (x2, y2) is calculated using the formula slope (m) = (y2 - y1) / (x2 - x1). Applying this formula to the points (-7,8) and (-7,0), the calculation would be (0 - 8) / (-7 + 7) which leads to a denominator of 0. This indicates that we have a vertical line, and the concept of slope does not apply (some may say it is undefined or infinite). Therefore, it is neither positive slope nor negative slope, contradicting options a and b.
As for the second question, using the points (1, 0.1) and (7, 26.8), the slope calculation would be (26.8 - 0.1) / (7 - 1) which simplifies to 26.7 / 6, giving us a slope of 4.45, making option b correct.
The appearance of a line's slope can be described as follows: A line with a positive slope goes upward to the right, a line with a negative slope goes downward to the right, and a line with a zero slope is horizontal.