What is the slope of the line that passes through the points left parenthesis, 9, comma, 4, right parenthesis(9,4) and left parenthesis, 3, comma, 9, right parenthesis(3,9)? Write your answer in simplest form.

To find the slope of a line that passes through two given points, you can use the slope formula:

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

Given the points \((9, 4)\) and \((3, 9)\), we can assign the coordinates as follows:

- \((x_1, y_1) = (9, 4)\)
- \((x_2, y_2) = (3, 9)\)

Substituting these values into the slope formula:

\[
m = \frac{9 - 4}{3 - 9}
\]

\[
m = \frac{5}{-6}
\]

\[
m = -\frac{5}{6}
\]

So, the slope of the line that passes through the points \((9, 4)\) and \((3, 9)\) is:

\[
m = -\frac{5}{6}
\]

This slope is already in its simplest form.

### Do you want more details or have any questions?

### Relative Questions:
1. How do you find the equation of the line given its slope and a point?
2. What does a negative slope indicate about the direction of a line?
3. How do you find the y-intercept of a line if you have the slope and a point?
4. What is the slope of a horizontal line? 
5. Can two points determine a unique line in a plane?

### Tip:
When calculating the slope, always pay attention to the order of subtraction to maintain the correct sign.

Learn how to calculate the slope of a line passing through the points (9, 4) and (3, 9) using the slope formula. This problem covers key concepts in coordinate geometry and linear equations. Suitable for Grades 7-9.

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