Final answer:
The slope for a line through points (1, 0.1) and (7, 26.8) is calculated as 4.45. The perpendicular slope is -1/4.45. Plot the given points and use the slopes to sketch the corresponding lines for both the original and the perpendicular lines.
Step-by-step explanation:
The question relates to plotting points and identifying slopes for lines on a graph in mathematics. To find the original slope of a line passing through two given points, (1, 0.1) and (7, 26.8), we use the slope formula:
m = (y2 - y1) / (x2 - x1)
This gives us (26.8 - 0.1) / (7 - 1) = 26.7 / 6 = 4.45. The perpendicular slope is the negative reciprocal of the original slope. For 4.45, the perpendicular slope would be -1/4.45. Points to plot for the original line could be the given points, (1, 0.1) and (7, 26.8), while additional points for the perpendicular line can be determined by using the perpendicular slope and any point it passes through. As for the graphs provided in Figure 12.4, we understand that a positive b value results in a line sloping upward, b equals 0 results in a horizontal line, and a negative b value results in a line sloping downward.