Find the equation of the line using the point-slope formula. Passes through the point \( (-7,8) \) and is parallel to the graph \( y=\frac{6}{7} x+4 \). ?

To find the equation of the line, we first identify the slope of the line we want to be parallel to. The slope of the line given by \( y = \frac{6}{7}x + 4 \) is \( \frac{6}{7} \). Since parallel lines have the same slope, the slope of our desired line is also \( \frac{6}{7} \). Using the point-slope formula, which is \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point the line passes through, we can substitute in our values. Here, \( m = \frac{6}{7} \), \( x_1 = -7 \), and \( y_1 = 8 \): \[ y - 8 = \frac{6}{7}(x - (-7)) \] \[ y - 8 = \frac{6}{7}(x + 7) \] This gives us the equation of the line in point-slope form. To convert it into slope-intercept form, you can simplify: \[ y - 8 = \frac{6}{7}x + 6 \] \[ y = \frac{6}{7}x + 14 \] So, the equation of the line is \( y = \frac{6}{7}x + 14 \).