Final answer:
To find the equation of a line perpendicular to the given line y=2x-4 through the point (0,-7), use the point-slope form of a linear equation. The equation of the perpendicular line is y + 7 = -1/2x.
Step-by-step explanation:
To find the equation of a line perpendicular to the given line, we need to determine the slope of the given line and then use the fact that perpendicular lines have slopes that are negative reciprocals of each other. The given line has a slope of 2. The negative reciprocal of 2 is -1/2. Since the line passes through the point (0,-7), we can use the point-slope form of a linear equation to find the equation of the perpendicular line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the values into the equation, we get: y - (-7) = -1/2(x - 0). Simplifying the equation, we get: y + 7 = -1/2x.