Final answer:
To find the y-intercept of the line segment AB given the coordinates of A (14, -1) and B (2, 1), calculate the slope and use one of the points with the slope to determine the y-intercept, which is found to be 4/3.
Step-by-step explanation:
Finding the y-intercept of Line AB
To find the y-intercept of the line segment AB with given points A (14, -1) and B (2, 1), we first need to find the slope (m) of the line. The slope formula is m = (y2 - y1) / (x2 - x1), which gives us:
m = (1 - (-1)) / (2 - 14) = 2 / (-12) = -1/6
Now that we have the slope, we can use either point and the slope to find the equation of the line in the slope-intercept form y = mx + b. Using point B (2, 1):
1 = (-1/6)(2) + b
1 = -1/3 + b
b = 1 + 1/3
b = 4/3
The y-intercept of AB is therefore 4/3, which means the line crosses the y-axis at the y-coordinate 4/3.