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To solve problem 10 from the uploaded image, we need to find the distance of the point \( P(-1, 3) \) from the line \( 3x - y = 5 \).

The distance \( d \) from a point \( (x_1, y_1) \) to a line \( Ax + By + C = 0 \) is given by the formula:
\[ d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}} \]

In this case, the point \( P \) is \((-1, 3)\) and the line equation is \( 3x - y - 5 = 0 \).

Here,
\[ A = 3, \, B = -1, \, C = -5 \]
\[ x_1 = -1, \, y_1 = 3 \]

Plugging in these values, we get:
\[ d = \frac{|3(-1) + (-1)(3) - 5|}{\sqrt{3^2 + (-1)^2}} \]
\[ d = \frac{|-3 - 3 - 5|}{\sqrt{9 + 1}} \]
\[ d = \frac{|-11|}{\sqrt{10}} \]
\[ d = \frac{11}{\sqrt{10}} \]
\[ d = \frac{11\sqrt{10}}{10} \]

Therefore, the distance of the point \( P(-1, 3) \) from the line \( 3x - y = 5 \) is \( \frac{11\sqrt{10}}{10} \).

Would you like more details or have any questions?

Here are 5 questions you might find interesting:
1. How do you derive the distance formula from a point to a line?
2. What is the geometric interpretation of the distance formula from a point to a line?
3. How do you find the perpendicular distance between parallel lines?
4. What is the significance of the absolute value in the distance formula?
5. How do you convert a general linear equation to slope-intercept form?

**Tip:** Always double-check your calculations when using formulas to avoid simple arithmetic errors.

Learn how to calculate the distance of point (-1, 3) from the line 3x - y = 5 using the distance formula. This problem involves applying the distance formula in analytic geometry to find the perpendicular distance from a point to a line. Suitable for high school students.

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