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.