To find the y-intercept of the line segment AB, we first need to determine the equation of the line passing through points A (4, 7) and B (6, 3).

Step 1: Find the slope of the line

The slope $m$ is calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the coordinates of points A and B: $m = \frac{3 - 7}{6 - 4} = \frac{-4}{2} = -2$

Step 2: Use the point-slope form of a line

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ Using point A (4, 7) and the slope $m = -2$: $y - 7 = -2(x - 4)$ Simplify the equation: $y - 7 = -2x + 8$ $y = -2x + 15$

Step 3: Find the y-intercept

The y-intercept occurs when $x = 0$. Substitute $x = 0$ into the equation: $y = -2(0) + 15 = 15$

Thus, the y-intercept of line AB is $15$.

Would you like further explanation or any clarifications?

Here are 5 related questions:

1. How do you find the x-intercept of a line given two points?
2. What is the distance between points A and B?
3. How would the slope change if A and B were swapped?
4. What is the midpoint of the line segment AB?
5. How do you calculate the length of the line segment AB?

Tip: When finding the y-intercept, always set $x = 0$ in the equation of the line!