Answer: To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the slope of the original line and use the point-slope form of a line.
The equation of the original line is 5y = 2x - 4, which we can rearrange to get y = (2/5)x - 4/5. The slope of this line is 2/5. The negative reciprocal of the slope is -5/2.
Now, we can use the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the slope -5/2 and the point (0, 7), we get:
y - 7 = -5/2 (x - 0)
y - 7 = -5/2 x
y = -5/2 x + 7
So the equation of the line perpendicular to 5y = 2x - 4 and passing through (0, 7) is y = -5/2 x + 7.
Explanation: