Final answer:
To find the equation of a line perpendicular to y=-2/7x/9 and passing through the point (4,-6), we determine the slope of the given line and use the point-slope form to write the equation of the perpendicular line.
Step-by-step explanation:
To find the equation of a line that is perpendicular to y=-2/7x/9 and passes through the point (4,-6), we need to determine the slope of the given line. The given line has a slope of -2/7. The slope of a line perpendicular to this line can be found by taking the negative reciprocal of -2/7, which is 7/2.
Using the point-slope form y - y1 = m(x - x1), we can substitute the slope and the coordinates of the given point into the equation. Therefore, the equation of the line perpendicular to y=-2/7x/9 and passing through (4,-6) is y - (-6) = (7/2)(x - 4).