Final answer:
The slope of the line passing through the points (-5/2, 1) and (-1/2, 4) in the xy-plane is 3/2.
Step-by-step explanation:
The question asks about calculating the slope of a line in the xy-plane that passes through two given points. The formula for the slope, m, when given two points (x₁, y₁) and (x₂, y₂), is m = (y₂ - y₁) / (x₂ - x₁). To find the slope of the line passing through the points (-5/2, 1) and (-1/2, 4), we use this formula.
Step 1: Identify the coordinates of the two points. Point 1 is (-5/2, 1) and Point 2 is (-1/2, 4).
Step 2: Apply the slope formula. m = (4 - 1) / (-1/2 - (-5/2)) = 3 / 2.
Therefore, the slope of the line passing through the points (-5/2, 1) and (-1/2, 4) is 3/2, which is the rate of change of y with respect to x on the line.