Final answer:
The slopes of lines in Set A and Set B are both -2/3, meaning they are decreasing lines. The slope for the line passing through points (1, 0.1) and (7, 26.8) is approximately 4.5. Positive, negative, and zero slopes determine whether a line will be increasing, decreasing, or horizontal.
Step-by-step explanation:
The slope of a line passing through two points can be calculated using the formula (y2 - y1) / (x2 - x1). Using this formula, we can find the slopes of the lines for Set A and Set B. For Set A, with points (0,4) and (6,0), the slope is (0 - 4) / (6 - 0) = -4 / 6 = -2/3. For Set B, with points (-3,6) and (6,0), the slope is (0 - 6) / (6 - (-3)) = -6 / 9 = -2/3. Therefore, both Set A and Set B have the same slope of -2/3, despite having different points. This implies that both lines are parallel, and each will be a straight line with a negative slope, indicating they are both decreasing lines.
Concerning the example in the question, the slope for the line passing through points (1, 0.1) and (7, 26.8) can be calculated as (26.8 - 0.1) / (7 - 1) = 26.7 / 6, which equals 4.45 or approximately 4.5. Therefore, the correct answer is 'b. 4.5'.
Examining the appearance of slopes further, a positive slope represents an increasing line, which means as x values increase, y values also increase. A negative slope, such as what we see with the slopes of Set A and Set B, means that as x values increase, y values decrease, showcasing a decreasing line. A slope of zero indicates a horizontal line with no rise or fall regardless of the change in x values.