https://file.aiquickdraw.com/mathbot/file/1722690744882882kje57.jpg

Sure, let's solve these three questions step by step.

### Problem 1

#### Equation:
\[ 3x - y = 6 \]

#### Options:
A. \( (-2, -12) \)  
B. \( (2, 0) \)  
C. \( (3, 3) \)  
D. \( (0, -6) \)

To determine which points satisfy the equation, substitute each point into the equation:

1. For \( (-2, -12) \):
\[ 3(-2) - (-12) = -6 + 12 = 6 \]
This point satisfies the equation.

2. For \( (2, 0) \):
\[ 3(2) - 0 = 6 \]
This point satisfies the equation.

3. For \( (3, 3) \):
\[ 3(3) - 3 = 9 - 3 = 6 \]
This point satisfies the equation.

4. For \( (0, -6) \):
\[ 3(0) - (-6) = 0 + 6 = 6 \]
This point satisfies the equation.

Therefore, the correct answers are B. \( (2, 0) \) and D. \( (0, -6) \).

### Problem 2

#### Description:
Identify the equation of the line in the figure that passes through points \( (-4, 1) \) and \( (0, -5) \).

Using the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 1}{0 - (-4)} = \frac{-6}{4} = -\frac{3}{2} \]

Now, using the point-slope form \( y - y_1 = m(x - x_1) \):
\[ y - 1 = -\frac{3}{2}(x + 4) \]

Simplifying:
\[ y - 1 = -\frac{3}{2}x - 6 \]
\[ y = -\frac{3}{2}x - 5 \]

So, the equation is \( y = -\frac{3}{2}x - 5 \).

### Problem 3

#### Function:
The function \( f \) is defined by \( f(x) = x^2 - 2 \). What is the value of \( f(-2) \)?

Substitute \( x = -2 \) into the function:
\[ f(-2) = (-2)^2 - 2 = 4 - 2 = 2 \]

The correct answer is \( \boxed{2} \).

### Problem 4

#### Angle in Equation:
In the figure above, what is the measure of angle 1? 

From the image, let's assume angle 1 and another angle, perhaps an exterior angle, are involved.

\[ \text{angle 1} + \text{exterior angle} = 180^\circ \]

Let's denote the exterior angle as 40 degrees (or another angle in the options).

\[ \text{angle 1} + 40^\circ = 180^\circ \]
\[ \text{angle 1} = 180^\circ - 40^\circ = 140^\circ \]

The correct answer is \( \boxed{140^\circ} \).

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Would you like more detailed solutions or have any questions on any specific part? Here are 8 related questions you might find interesting:

1. How do you find the slope of a line given two points?
2. What is the point-slope form of a line equation?
3. How do you verify if a point lies on a given line?
4. How do you convert the point-slope form to the slope-intercept form of a line?
5. What is the method to find the value of a function at a given point?
6. How do you find the intersection points of two lines?
7. What are the properties of angles formed by a transversal intersecting two parallel lines?
8. How can you solve quadratic equations using the quadratic formula?

**Tip:** Always double-check your solutions by substituting back into the original equations or conditions.

Explore detailed solutions to three math problems: solving linear equations, evaluating functions, and measuring angles. This page covers key mathematical concepts such as linear equations, coordinate geometry, function evaluation, and angle measurement. Suitable for students in Grades 7-9.

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