Solutions:

7) Find the distance between $(7, 6)$ and $(0, 2)$:

We use the distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ Substitute the points $(x_1, y_1) = (7, 6)$ and $(x_2, y_2) = (0, 2)$: $d = \sqrt{(0 - 7)^2 + (2 - 6)^2} = \sqrt{(-7)^2 + (-4)^2} = \sqrt{49 + 16} = \sqrt{65} \approx 8.06$ Answer: $8.06$

8) Find the distance between $(4, 2)$ and $(-6, -6)$:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ Substitute $(x_1, y_1) = (4, 2)$ and $(x_2, y_2) = (-6, -6)$: $d = \sqrt{(-6 - 4)^2 + (-6 - 2)^2} = \sqrt{(-10)^2 + (-8)^2} = \sqrt{100 + 64} = \sqrt{164} \approx 12.81$ Answer: $12.81$

9) Find the distance between $(-6, 1)$ and $(-3, 1)$:

Since the y-coordinates are the same, the distance is simply the difference in x-coordinates: $d = |x_2 - x_1| = |-3 - (-6)| = |-3 + 6| = 3$ Answer: $3$

10) Find the distance between $(-3, 6)$ and $(2, 1)$:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ Substitute $(x_1, y_1) = (-3, 6)$ and $(x_2, y_2) = (2, 1)$: $d = \sqrt{(2 - (-3))^2 + (1 - 6)^2} = \sqrt{(2 + 3)^2 + (-5)^2} = \sqrt{5^2 + (-5)^2} = \sqrt{25 + 25} = \sqrt{50} \approx 7.07$ Answer: $7.07$

11) Slope of the line in the graph:

From the graph, the points are approximately $(4, 3)$ and $(-3, -2)$. Slope $m$ is: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 3}{-3 - 4} = \frac{-5}{-7} = \frac{5}{7}$ Answer: $\frac{5}{7}$

12) Slope of the line in the graph:

From the graph, the points are approximately $(2, 3)$ and $(-3, -1)$. $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 3}{-3 - 2} = \frac{-4}{-5} = \frac{4}{5}$ Answer: $\frac{4}{5}$

13) Slope of the line in the graph:

From the graph, the points are approximately $(-2, -1)$ and $(2, -3)$. $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - (-1)}{2 - (-2)} = \frac{-3 + 1}{2 + 2} = \frac{-2}{4} = -\frac{1}{2}$ Answer: $-\frac{1}{2}$

14) Slope of the line in the graph:

From the graph, the points are approximately $(3, 1)$ and $(-2, -2)$. $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 1}{-2 - 3} = \frac{-3}{-5} = \frac{3}{5}$ Answer: $\frac{3}{5}$

Do you need additional clarifications or a more detailed explanation of any solution?
Here are five related questions for further practice:

1. How do you calculate the midpoint between two points?
2. What is the equation of a line given two points?
3. How can you tell if two lines are perpendicular?
4. What is the formula for calculating the slope of a horizontal line?
5. How does the distance formula relate to the Pythagorean theorem?

Tip: Always double-check your calculations, especially signs, when applying the distance or slope formulas!