To find the equation of the line that passes through the points \((-2, 3)\) and \((0, -7)\), we first need to determine the slope (m) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let \((x_1, y_1) = (-2, 3)\) and \((x_2, y_2) = (0, -7)\):
\[ m = \frac{-7 - 3}{0 - (-2)} = \frac{-10}{2} = -5 \]
Now that we have the slope \(m = -5\), we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
Using the point \((0, -7)\) (you could also use \((-2, 3)\)), we have:
\[ y - (-7) = -5(x - 0) \]
This simplifies to:
\[ y + 7 = -5x \]
Now, we can rearrange this into slope-intercept form \(y = mx + b\):
\[ y = -5x - 7 \]
Thus, the equation of the line that passes through the points \((-2, 3)\) and \((0, -7)\) is:
\[ y = -5x - 7 \]