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

The slope \( m \) of a line segment joining two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

In this problem, the two points are \((3, 2)\) and \((4, y)\), and the slope \( m \) is given as \(-3\).

Substituting the given values into the slope formula:

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

Simplifying:

\[
-3 = y - 2
\]

Now, solve for \( y \):

\[
y = -3 + 2 = -1
\]

So, \( y = -1 \).

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Find the slope of the line passing through the points \((2, 5)\) and \((6, 3)\).
2. If the slope of a line is 2 and it passes through the point \((1, 4)\), find the equation of the line.
3. What is the slope of the line perpendicular to the line joining the points \((0, 0)\) and \((2, 4)\)?
4. Determine the equation of a line with slope \(-2\) that passes through the point \((3, -1)\).
5. If two points on a line are \((x_1, y_1)\) and \((x_2, y_2)\), write the general formula for the slope.

**Tip**: When solving for the slope between two points, remember that the order in which you subtract coordinates matters; always subtract in the same direction for both the \(x\)-coordinates and the \(y\)-coordinates.

Learn how to find the missing coordinate 'y' when given the slope of a line segment joining two points (3, 2) and (4, y). This problem involves algebraic concepts such as slope calculation and solving linear equations, making it ideal for students in Grades 8-10.

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