https://file.aiquickdraw.com/mathbot/file/1726513415420i666cr26.jpg

Let's analyze the graph and solve the questions.

### Part A:
The blue line is horizontal and intersects the y-axis at \( y = 3 \). This means that for all values of \( x \), the value of \( y \) remains constant at 3. Therefore, the equation of the blue line is:

\[ y = 3 \]

The correct answer for Part A is **\( y = 3 \)**.

### Part B:
The red line appears to be slanted and follows a downward slope, passing through two points, such as \((0, 2)\) and \((1, -1)\). To determine the equation of the line, we need to calculate the slope (m) and the y-intercept (b) using the slope-intercept form \( y = mx + b \).

- The slope \( m \) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3
\]

- The y-intercept \( b \) is the point where the line crosses the y-axis, which is at \( (0, 2) \). So, \( b = 2 \).

Thus, the equation of the red line is:

\[ y = -3x + 2 \]

The correct answer for Part B is **\( y = -3x + 2 \)**.

### Domain of \( f(x) \):
The domain is the combination of the x-values where the blue and red lines exist. Since the blue line extends horizontally, and the red line is a diagonal line, the domain is the union of the x-values from both lines.

Would you like further clarification or more details on these steps?

Here are 5 questions that expand on this concept:
1. How do you determine the slope of a line from two points?
2. What is the general form of the equation of a line?
3. How do you calculate the domain and range of a function from a graph?
4. What are horizontal and vertical lines, and how are their equations represented?
5. How do you find the point where two lines intersect?

**Tip:** When analyzing linear equations, always look for points where the lines cross the axes to identify slopes and intercepts easily.

We want to define a function that is represented by this graph y = f(x). A) If the blue line (using its pattern) continued on forever, the full line would represent the graph of which equation: (x = -2, y = -2, y = 3, x = 3). B) If the red line (using its pattern) continued on forever, the full line would represent the graph of which equation: (y = x ± 4, x = 2, y = -4, y = -3x + 2).

Analyze a graph with a horizontal blue line and a slanted red line to find their respective equations. Learn how to apply the slope-intercept form and the slope formula to determine the correct equations. Suitable for students in Grades 7-10.

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