Question

Which equation describes this line?
$（l, 13, 10
(-2, 4) °
• 4 - 2 = 3(x - 4)
• y- 4 = 3(*+ 3(x+2)
0y- 1 = 3(x - 13).
• y - 4 = 3 (x - 2)

Answer 1

To determine which equation describes the line, we will analyze the given equations in terms of their forms.

1. **Equation 1: \(y - 4 = 3(x + 2)\)**
- This can be rewritten in slope-intercept form, \(y = mx + b\):
\[
y - 4 = 3(x + 2) \implies y - 4 = 3x + 6 \implies y = 3x + 10
\]

2. **Equation 2: \(y - 1 = 3(x - 13)\)**
- Rewriting this gives:
\[
y - 1 = 3(x - 13) \implies y - 1 = 3x - 39 \implies y = 3x - 38
\]

3. **Equation 3: \(y - 4 = 3(x - 4)\)**
- Rewriting gives:
\[
y - 4 = 3(x - 4) \implies y - 4 = 3x - 12 \implies y = 3x - 8
\]

4. **Equation 4: \(y - 4 = 3(x + 3)\)**
- Rewriting gives:
\[
y - 4 = 3(x + 3) \implies y - 4 = 3x + 9 \implies y = 3x + 13
\]

5. **Equation 5: \(y - 4 = 3(x - 2)\)**
- Rewriting gives:
\[
y - 4 = 3(x - 2) \implies y - 4 = 3x - 6 \implies y = 3x - 2
\]

Now, let's summarize:

- **Equation 1:** \(y = 3x + 10\)
- **Equation 2:** \(y = 3x - 38\)
- **Equation 3:** \(y = 3x - 8\)
- **Equation 4:** \(y = 3x + 13\)
- **Equation 5:** \(y = 3x - 2\)

The slope of each of these lines is \(3\), and they differ by the y-intercepts.

To choose the correct equation that describes the line, we need additional context or coordinates through which the line passes. Given no extra points but taking a look at the formats suggests that any of the equations could describe some line with the slope of 3 if such a line passes through the respective points from which they are derived.

If you have specific points or additional context that should be considered, please provide that, and we can find the exact line representing those points.