https://file.aiquickdraw.com/mathbot/file/17261813417378hw5v7r2.jpg

Let's solve this by analyzing the graph.

### Step 1: Find the slope of the line
The line passes through the points \((0, 4)\) (y-intercept) and \((2, -2)\). To find the slope \(m\), use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the points \((0, 4)\) and \((2, -2)\):
\[
m = \frac{-2 - 4}{2 - 0} = \frac{-6}{2} = -3
\]

### Step 2: Write the equation of the line in slope-intercept form
The slope-intercept form of a line is:
\[
y = mx + b
\]
Where \(m = -3\) and \(b = 4\) (from the y-intercept \((0, 4)\)):
\[
y = -3x + 4
\]

### Step 3: Analyze the given options
Now that we know the slope is \(-3\) and the y-intercept is 4, let's check the options:

1. **\(y = -3x + 4\)**: This is correct. The slope is \(-3\) and the y-intercept is 4.
2. **\(y = 3x + 4\)**: Incorrect, the slope is positive here.
3. **\(y - 1 = -3(x - 1)\)**: Let's simplify this. Distribute the \(-3\):
   \[
   y - 1 = -3x + 3 \quad \Rightarrow \quad y = -3x + 4
   \]
   This matches the correct equation, so this is correct.
4. **\(y - 1 = 3(x - 1)\)**: Let's simplify this. Distribute the 3:
   \[
   y - 1 = 3x - 3 \quad \Rightarrow \quad y = 3x - 2
   \]
   This does not match the correct equation, so this is incorrect.
5. **\(3x + y = 4\)**: Let's rearrange this to the slope-intercept form \(y = mx + b\):
   \[
   y = -3x + 4
   \]
   This matches the correct equation, so this is correct.

### Correct answers:
- \(y = -3x + 4\)
- \(y - 1 = -3(x - 1)\)
- \(3x + y = 4\)

Would you like further details or clarifications? Here are some related questions:

1. How can we derive the equation of a line using two points?
2. What is the general form of a linear equation, and how does it relate to the slope-intercept form?
3. What happens to the slope when a line is vertical or horizontal?
4. How can you determine the slope from a graph without explicit points?
5. How do transformations (translations or scaling) affect the equation of a line?

**Tip**: Always confirm the slope of a line from its direction on the graph; a downward-sloping line has a negative slope.

Meara drew a graph of a linear function. What is the equation of the line?

Analyze a linear graph to determine its equation. Learn to calculate the slope and find the correct form of the line equation. This problem is suitable for Grades 8-10 and covers algebraic concepts including slope and slope-intercept form.

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