Question

Which equation describes this line?（l, 13)
(-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 passing through the points \( (l, 13) \) and \( (-2, 4) \), we first need to find the slope of the line and then use the point-slope form of the equation.

1. **Calculate the slope (m)** using the two points \( (x_1, y_1) = (l, 13) \) and \( (x_2, y_2) = (-2, 4) \):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 13}{-2 - l} = \frac{-9}{-2 - l}
\]

2. We need to simplify the point-slope form. Since we don't have the value of \( l \), and assuming we have a general form with the slope of \( 3 \) from the provided answers, we use:
\[
y - 4 = 3(x + 2) \, \text{(one of the provided equations)}
\]
This means that we assume the slope is 3, and we can redefine our \( y - 4 = 3(x + 2) \).

3. For the points to be consistent with a slope of 3, we simplify:
\[
y - 4 = 3(x + 2)
\]
Expanding this gives:
\[
y - 4 = 3x + 6 \\
y = 3x + 10
\]

4. Now check if both points satisfy this equation:
- For point \( (-2, 4) \):
\[
y = 3(-2) + 10 = -6 + 10 = 4 \quad \text{(satisfied)}
\]
- For point \( (l, 13) \):
\[
13 = 3l + 10 \\
3l = 3 \\
l = 1
\]

Thus, the line equation we have \( y - 4 = 3(x + 2) \) is correct, with \( l = 1 \).

Therefore, the correct answer from the options provided is:
**y - 4 = 3(x + 2)**