Final answer:
The equation of the line perpendicular to -2x + 4y = 8 and passing through the point (-2,4) is y = -2x.
Step-by-step explanation:
We have to find the equation of a line that is perpendicular to another line. The original equation is given by -2x + 4y = 8. To find a perpendicular line, we need to determine the slope of the given line and then find the negative reciprocal of that slope for our new line. First, we rearrange the given equation into slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
The given line -2x + 4y = 8 can be written as 4y = 2x + 8, which simplifies to y = (1/2)x + 2. Therefore, the slope of the given line is 1/2. The negative reciprocal of 1/2 is -2. Now, we use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Since our line passes through the point (-2, 4) and has a slope of -2, we have y - 4 = -2(x + 2). Simplifying this equation, we get y = -2x - 4 + 4, which results in y = -2x as the equation of the perpendicular line.