find the slope for an equation for a line passing thru the points (-2,4) and (4,-5)

To find the slope of a line passing through two points, \((-2, 4)\) and \((4, -5)\), we use the slope formula:

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

where \((x_1, y_1) = (-2, 4)\) and \((x_2, y_2) = (4, -5)\).

Substituting the values:

\[
m = \frac{-5 - 4}{4 - (-2)}
\]

\[
m = \frac{-9}{6}
\]

\[
m = -\frac{3}{2}
\]

So, the slope of the line passing through the points \((-2, 4)\) and \((4, -5)\) is:

\[
\boxed{-\frac{3}{2}}
\]

Would you like to see more details or have any questions? Here are some related problems:

1. Find the slope of a line passing through the points \((3, 7)\) and \((6, 2)\).
2. Determine the slope of a horizontal line passing through any two points.
3. What is the slope of a vertical line?
4. Find the equation of a line passing through \((-2, 4)\) and \((4, -5)\).
5. Calculate the slope of the line passing through the points \((0, 0)\) and \((5, 10)\).

**Tip:** The slope of a line measures how steep the line is. A negative slope indicates the line goes down from left to right.

Learn how to find the slope of a line passing through the points (-2, 4) and (4, -5). This problem covers key concepts in analytic geometry, using the slope formula. Suitable for students in Grades 8-10.

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