Final answer:
To find the equation of a line perpendicular to another line, find the negative reciprocal of the original line's slope. The equation of line g is y = -4x + 2.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, we need to find the negative reciprocal of the original line's slope. The given equation of line f is y = 1/4x + 2. The slope of line f is 1/4. The negative reciprocal of 1/4 is -4. Therefore, the equation of line g is y = -4x + b, where b is the y-intercept of line g.
To find the y-intercept, we can use the fact that line g passes through the same point as line f. Plug in the coordinates of a point on line f (such as the y-intercept) into the equation of line f and solve for y. The equation becomes 2 = 1/4*0 + y, which simplifies to y = 2. Therefore, the y-intercept of line g is also 2. Thus, the equation of line g is y = -4x + 2.