Final answer:
The equation of the line perpendicular to y = 0.25x - 7 and passing through the point (-6, 8) is y = -4x - 16.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line y = 0.25x - 7 and passes through the point (-6, 8), we must first determine the slope of the new line. The slope of the given line is 0.25; therefore, the slope of a line perpendicular to it will be the negative reciprocal, which is -4 (since -1/0.25 = -4). With this slope and the point (-6, 8), we can use the point-slope form of the linear equation, which is y - y1 = m(x - x1), to find our equation. Substituting the given point and slope we have:
y - 8 = -4(x + 6)
Simplifying this equation gives us:
y - 8 = -4x - 24
Adding 8 to both sides results in the final equation:
y = -4x - 16