Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line. Containing the points \( (-3,6) \) and \( (-1,7) \) The equation is (Type an equation. Simplify your answer.)

To find the equation of the line containing the points \((-3,6)\) and \((-1,7)\), we start by calculating the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\): \[ m = \frac{7 - 6}{-1 - (-3)} = \frac{1}{2} \] Next, we can use the slope-intercept form \(y = mx + b\) to find the y-intercept \(b\). Using point \((-3,6)\): \[ 6 = \frac{1}{2}(-3) + b \] \[ 6 = -\frac{3}{2} + b \] \[ b = 6 + \frac{3}{2} = \frac{12}{2} + \frac{3}{2} = \frac{15}{2} \] Now we have the slope and y-intercept. The equation of the line is: \[ y = \frac{1}{2}x + \frac{15}{2} \] Thus, the equation can be expressed as: \[ y = \frac{1}{2}x + \frac{15}{2} \]