Final answer:
The equation of the line passing through (8, -2) and perpendicular to the line y = 1/4x + 2 is y + 2 = -4(x - 8) in point-slope form, which can be simplified to y = -4x + 34 in slope-intercept form.
Step-by-step explanation:
The student's question involves finding the equation of a line in both point-slope form and slope-intercept form.
Given the line is perpendicular to the line whose equation is y = 1/4x + 2, the slope of the perpendicular line will be the negative reciprocal of 1/4 which is -4. The point through which the new line passes is (8, -2).
Using the point-slope form, the equation can be written as y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the point the line passes through.
Thus, with m = -4 and the point (8, -2), the equation becomes y + 2 = -4(x - 8).
For the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we can simplify the point-slope form to get the slope-intercept form.
Expanding y + 2 = -4(x - 8), we get y = -4x + 34, where -4 is the slope, and 34 is the y-intercept.
The complete question is:content loaded
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form Passing through (8, -2) and perpendicular to the line whose equation is y = 1/4x +2