Final answer:
To find the equation of a line that is perpendicular to y = 4x + 2 and passes through a given point, we can use the point-slope form of a line.
Step-by-step explanation:
To find the equation of a line that is perpendicular to y = 4x + 2 and passes through the point (-8,5),
we need to use the fact that perpendicular lines have negative reciprocal slopes.
The slope of the given line is 4, so the slope of the perpendicular line is -1/4.
We can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we get y - 5 = -1/4(x - (-8)).
Simplifying the equation, we get y - 5 = -1/4(x + 8) and further simplifying, y - 5 = -1/4x - 2.
Rearranging the equation in intercept form, we get y = -1/4x - 2 + 5, which simplifies to y = -1/4x + 3.