The coordinates of A and B are(4,7) and (6,3) what is the intercept of AB on the y-axis

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!

The coordinates of A and B are (4, 7) and (6, 3). What is the intercept of AB on the y-axis?

Learn how to find the y-intercept of a line passing through two points (4, 7) and (6, 3) with a step-by-step solution. This problem involves key concepts in analytic geometry, including calculating the slope and using the point-slope form of a line. Suitable for students in Grades 8-10.

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