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.