With slope \( -\frac{7}{8} \), through \( \left(0, \frac{9}{7}\right. \)

To find the equation of a line with a given slope and a point it passes through, we can use the point-slope form of the equation of a line, which is given by: \[ y - y_1 = m(x - x_1) \] where: - \( m \) is the slope, - \( (x_1, y_1) \) is the point the line passes through. In this case, the slope \( m = -\frac{7}{8} \) and the point is \( (0, \frac{9}{7}) \). Let's substitute these values into the point-slope form: 1. Identify \( x_1 \) and \( y_1 \): - \( x_1 = 0 \) - \( y_1 = \frac{9}{7} \) 2. Substitute into the equation: \[ y - \frac{9}{7} = -\frac{7}{8}(x - 0) \] This simplifies to: \[ y - \frac{9}{7} = -\frac{7}{8}x \] 3. Now, add \( \frac{9}{7} \) to both sides to solve for \( y \): \[ y = -\frac{7}{8}x + \frac{9}{7} \] This is the equation of the line in slope-intercept form. If you need further manipulation or a different form of the equation, please let me know!