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.