Final answer:
The equation of the line that is parallel to y = -6/7x + 3 and passes through the point (-5, 4) is y = -6/7x + 58/7.
Step-by-step explanation:
To find the equation of a line that is parallel to the line y = -6/7x + 3 and passes through the point (-5, 4), we first need to determine the slope of the given line. The slope of the line y = -6/7x + 3 is -6/7. Since a line parallel to the given line will have the same slope, the equation of the parallel line can be written as y = -6/7x + b, where b is the y-intercept of the line. To find the value of b, we substitute the coordinates of the given point into the equation and solve for b:
4 = (-6/7)(-5) + b
b = 4 + 30/7 = 58/7.
Therefore, the equation of the line that is parallel to y = -6/7x + 3 and passes through the point (-5, 4) is y = -6/7x + 58/7.