Final answer:
The slope of the line with points X and Y is calculated using the formula (Y2 - Y1) / (X2 - X1), using points (2,1) and (14,31) to obtain a slope of 2.5.
Step-by-step explanation:
To determine the slope of the line given two sets of points X and Y, we use the formula for the slope of a line, which is rise over run, or (Y2 - Y1) / (X2 - X1). To illustrate this, let's choose two points from the given sets. We'll pick the first and last points, (2,1) and (14,31), for calculation.
Let X1 = 2 and
Y1 = 1 for the first point.
Let X2 = 14 and
Y2 = 31 for the second point.
Substitute these values into the slope formula:
Slope (m) = (Y2 - Y1) / (X2 - X1)
= (31 - 1) / (14 - 2)
= 30 / 12
= 2.5.
Therefore, the slope of the line is 2.5, indicating that for every increase of 1 on the x-axis, the value on the y-axis rises by 2.5. The slope is consistent across the entire straight line.