Find an equation of the line containing the given pair of points. \[ (-2,0) \text { and }(0,7) \] An equation of the line is \( y=\square \)

To find the equation of the line containing the points \((-2, 0)\) and \((0, 7)\), we first need to determine the slope of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, we can assign the points as follows: - \((x_1, y_1) = (-2, 0)\) - \((x_2, y_2) = (0, 7)\) Now, substituting the values into the slope formula: \[ m = \frac{7 - 0}{0 - (-2)} = \frac{7}{0 + 2} = \frac{7}{2} \] Now that we have the slope \(m = \frac{7}{2}\), we can use the point-slope form of the equation of a line, which is given by: \[ y - y_1 = m(x - x_1) \] Using the point \((0, 7)\) (you can use either point), we substitute \(m\), \(x_1\), and \(y_1\): \[ y - 7 = \frac{7}{2}(x - 0) \] This simplifies to: \[ y - 7 = \frac{7}{2}x \] Now, we can solve for \(y\): \[ y = \frac{7}{2}x + 7 \] To express this in the form \(y = mx + b\), we can rewrite it as: \[ y = \frac{7}{2}x + 7 \] Thus, the equation of the line is: \[ y = \frac{7}{2}x + 7 \] So, the answer is: \[ y = \frac{7}{2}x + 7 \]