A line that is perpendicular to another line has a slope that is the negative reciprocal of the original line. The slope of the line y = 2/7x - 8 is 2/7. To find the slope of the line that is perpendicular to it, we take the negative reciprocal of 2/7 which is -7/2.
We know that the line we're trying to find passes through the point (-4, 2), so we can use this point and the slope to write the equation of the line in point-slope form:
y - y1 = m (x - x1)
where (x1, y1) is the point the line passes through, m is the slope, and y and x are the coordinates of any point on the line.
So the equation of the line that passes through (-4,2) and is perpendicular to the line y= 2/7x - 8 is:
y - 2 = -7/2 (x + 4)
Simplifying this, we get
y = -7/2 x - 8
Therefore the equation of the line that passes through (-4,2) and is perpendicular to the line y= 2/7x - 8 is y = -7/2 x - 8