find the distance from the point (9,5) to the line 4x-3y=-4.

To find the distance from a point to a line, you can use the distance formula:

\[
\text{Distance} = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}
\]

where \(Ax + By + C = 0\) is the equation of the line, and \((x_1, y_1)\) is the point.

For the given problem:
- The equation of the line is \(4x - 3y = -4\), which can be rewritten as \(4x - 3y + 4 = 0\). Here, \(A = 4\), \(B = -3\), and \(C = 4\).
- The point is \((9, 5)\), so \(x_1 = 9\) and \(y_1 = 5\).

Now, plug these values into the distance formula:

\[
\text{Distance} = \frac{|4(9) - 3(5) + 4|}{\sqrt{4^2 + (-3)^2}}
\]

Simplify the expression:

\[
\text{Distance} = \frac{|36 - 15 + 4|}{\sqrt{16 + 9}} = \frac{|25|}{\sqrt{25}} = \frac{25}{5} = 5
\]

So, the distance from the point \((9, 5)\) to the line \(4x - 3y = -4\) is **5 units**.

Would you like any additional details or have any questions? 

Here are five related questions you might find interesting:
1. How would you find the distance between two points on a plane?
2. What is the formula for the slope of a line between two points?
3. How do you find the equation of a line that is perpendicular to a given line?
4. What is the process to convert a general equation of a line to its slope-intercept form?
5. How can you determine if a point lies on a given line?

**Tip:** Always double-check your signs when substituting values into formulas, as a small mistake can change the entire result.

Learn how to find the distance from the point (9, 5) to the line 4x - 3y = -4 using the distance formula. Step-by-step solution provided with detailed calculations. Suitable for high school students.

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