Final answer:
The slope of the line described by the equation 2y = -4x - 6 is -2. Additionally, the slope of the line passing through the points (1, 0.1) and (7, 26.8) is 4.5.
Step-by-step explanation:
The slope of the line given by the equation 2y = -4x - 6 can be found by first writing it in slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept. To do so, divide every term by 2 to get y = -2x - 3. This reveals that the slope of the line is -2.
For the general knowledge, when we have two points, we can also determine the slope of the line that passes through them. Given two points (Point 1: (1, 0.1), Point 2: (7, 26.8)), we can use the formula slope = (y2 - y1) / (x2 - x1). Here, the slope would be (26.8 - 0.1) / (7 - 1), which simplifies to 26.7 / 6 = 4.45, rounded to 4.5 as the possible answer choices are to one decimal place. Thus, the slope for the line passing through these two points is indeed 4.5.