Final answer:
The equation of a line perpendicular to y = 0.25x - 7 that passes through (-6, 8) is y = -4x - 16. This is found by determining the negative reciprocal of the original slope, which is -4, and using the point-slope form with the given point to find the equation.
Step-by-step explanation:
To write the equation of a line that is perpendicular to y = 0.25x - 7 and passes through the point (-6, 8), we first need to find the slope of the given line. The equation y = 0.25x - 7 is in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. For the given equation, the slope m = 0.25. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the perpendicular line will be -4 (the negative reciprocal of 0.25).
Now, using the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope, we substitute the slope -4 and the point (-6, 8) to get:
y - 8 = -4(x + 6)
Distributing the slope through, we have y - 8 = -4x - 24. Adding 8 to both sides gives us the final equation in slope-intercept form:
y = -4x - 16