Final answer:
To find a line parallel to the one through (-2, -2.5) and (1, 0), one must calculate the slope of the initial line and use that same slope with a different y-intercept. The slope is 2.5/3, so any line with this slope will be parallel to the given line.
Step-by-step explanation:
The question is asking for a line that is parallel to the line passing through the points (-2, -2.5) and (1, 0). To determine if another line is parallel to this one, we need to find the slope of the line that goes through these points since parallel lines have the same slope. First, calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁). Plugging in the values from the points, we have m = (0 - (-2.5)) / (1 - (-2)) m = 2.5 / 3.
Any line with a slope of 2.5/3 will be parallel to the line through (-2, -2.5) and (1, 0). For example, if we choose another point (x, y) such that the line passing through this point and either of the provided points (-2, -2.5) or (1, 0) has the same slope of 2.5/3, then that line will be parallel. Remember that the general equation of a line is y = mx + b where m is the slope and b is the y-intercept. To find the equation of a line parallel to the given one, you only need to choose a different y-intercept (b). As an illustration, if we want a line parallel to the given one that passes through the point (0, 1), we would use the same slope of 2.5/3 and obtain the following equation: y = (2.5/3)x + 1. This line is parallel to the line through (-2, -2.5) and (1, 0) since they share the same slope.