Bot GPT 4-o mini To find the equation of the line passing through the points \((-2, 4)\) and \((1, 13)\), we first calculate the slope \(m\) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (-2, 4)\) and \((x_2, y_2) = (1, 13)\):
\[ m = \frac{13 - 4}{1 - (-2)} = \frac{9}{3} = 3 \]
Now we have the slope \(m = 3\).
Next, we can use the point-slope form of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
We can use either of the given points. Using point \((-2, 4)\):
\[ y - 4 = 3(x - (-2)) \] \[ y - 4 = 3(x + 2) \]
So, the equation in point-slope form is:
\[ y - 4 = 3(x + 2) \]
Now let's compare this to the options you provided:
- \(y - 4 = 3(x - 2)\)
- \(y - 2 = 3(x - 4)\)
- \(y - 4 = 3(x + 2)\)
- \(y - 1 = 3(x - 13)\)
The correct equation that describes the line passing through the points \((-2, 4)\) and \((1, 13)\) is:
\[ y - 4 = 3(x + 2) \]
Thus, the answer is option 3.
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