Final answer:
The slope for the line passing through points (1, 0.1) and (7, 26.8) is approximately 4.45, which is rounded to 4.5 to match the given options.
Step-by-step explanation:
The question is asking us to find the slope of a line that passes through two given points: Point 1 (1, 0.1) and Point 2 (7, 26.8). To calculate the slope, which we denote as m, we use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Applying the given coordinates to the formula results in m = (26.8 - 0.1) / (7 - 1), which simplifies to m = 26.7 / 6 or approximately m = 4.45. Therefore, the slope of the line passing through these two points is approximately 4.5, as this matches one of the given options closest.
Understanding slope is an essential part of the algebra of straight lines, and it defines the direction and steepness of the line. Illustrated in Figure A1, we see that a line with a slope of 3 and a y-intercept of 9 shows how slope and intercept determine a line's position and angle on a coordinate plane.