Bot GPT 4-o mini 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.
-
Calculate the slope (m) using the two points \( (x_1, y_1) = (l, 13) \) and \( (x_2, y_2) = (-2, 4) \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 13}{-2 - l} = \frac{-9}{-2 - l} \]
-
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 \( y - 4 = 3(x + 2) \).
-
For the points to be consistent with a slope of 3, we simplify: \[ y - 4 = 3(x + 2) \] Expanding this gives: \[ y - 4 = 3x + 6 \ y = 3x + 10 \]
-
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)
1 answer