Final answer:
To find the equation of the line that is perpendicular to y = (5/7)x + 6 and passes through the point (-15, 3), use the negative reciprocal of the slope of the given line and substitute the coordinates of the given point. The equation of the perpendicular line is y = (-7/5)x - (6/5).
Step-by-step explanation:
To find the equation of the line that is perpendicular to y = (5/7)x + 6 and goes through the point (-15, 3), we first need to determine the slope of the given line.
The equation of the given line is in the form y = mx + b, where m represents the slope. So, m = 5/7.
Since a line that is perpendicular to another line will have a negative reciprocal slope, the slope of the perpendicular line will be -7/5.
Using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values of the given point (-15, 3) to find the equation of the perpendicular line.
So, the equation of the line perpendicular to y = (5/7)x + 6 and passing through the point (-15, 3) is y = (-7/5)x - (6/5).