Final answer:
In point-slope form, the equation for a line with a slope of 1.9 through (4.5, -1.4) is y + 1.4 = 1.9(x - 4.5), and for a slope of 2 through (-8,1), it is y - 1 = 2(x + 8). The slope between (1, 0.1) and (7, 26.8) is approximately 4.5.
Step-by-step explanation:
The equation of the line in point-slope form that has a slope of 1.9 and passes through the point (4.5, -1.4) can be written as y - (-1.4) = 1.9(x - 4.5), which simplifies to y + 1.4 = 1.9(x - 4.5). For the line with a slope of 2 that passes through the point (-8,1), the equation is y - 1 = 2(x + 8), which simplifies to y - 1 = 2x + 16.
The slope, denoted as m, of a line passing through two points can be found using the formula m = (y2 - y1) / (x2 - x1). For points (1, 0.1) and (7, 26.8), the slope calculation would be m = (26.8 - 0.1) / (7 - 1), which equals 4.45 when rounded to two decimal places, so the correct answer is b. 4.5.