Find y if the slope of the line segment joining (3, 2) to (4, y) is -3.

To find \( y \), we use the formula for the slope of a line segment that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, the points given are \((3, 2)\) and \((4, y)\). So, 

\[
(x_1, y_1) = (3, 2), \quad (x_2, y_2) = (4, y)
\]

The slope is given as \(-3\). Substituting the values into the slope formula:

\[
-3 = \frac{y - 2}{4 - 3}
\]

Simplify the denominator:

\[
-3 = y - 2
\]

To solve for \( y \), add 2 to both sides:

\[
y = -3 + 2
\]

\[
y = -1
\]

So, the value of \( y \) is \(-1\).

### Would you like more details or have any questions?

Here are some related questions:
1. What is the formula for finding the slope between two points?
2. How do you find the equation of a line given a point and the slope?
3. How can you determine if two lines are parallel?
4. What does a negative slope indicate about the direction of a line?
5. How can you find the midpoint of a line segment joining two points?

**Tip:** When dealing with slope, always pay attention to the signs to determine the direction of the line.

Learn how to find the value of y given the slope of the line segment joining the points (3, 2) and (4, y) with a detailed step-by-step solution. This problem involves key concepts in algebra and coordinate geometry, focusing on the slope formula and is suitable for students in Grades 8-10.

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