Final answer:
To find the equation of the line perpendicular to the given line passing through (-2, -8), we use the point-slope form of a line. The equation of the line is y + 8 = 2(x + 2). By substituting a value for y, we can solve for x.
Step-by-step explanation:
To find the equation of the line perpendicular to the given line passing through (-2, -8), we first need to find the slope of the given line. The slope of the given line is calculated as (2-4)/(5-1) = -0.5. The line perpendicular to the given line will have a slope equal to the negative reciprocal of this slope, which is 2. So, the equation of the perpendicular line in point-slope form can be written as y - y1 = m(x - x1), where (x1, y1) is the point (-2, -8) and m is the slope 2. Substituting these values, we get y + 8 = 2(x + 2). Now, we can solve for x by substituting any value of y and solving for x. For example, if we use y = -1, we can solve for x as -1 + 8 = 2(x + 2), which simplifies to 7 = 2x + 4. By isolating x, we get x = (7 - 4) / 2 = 1.5.