Final answer:
To find the equation of a line perpendicular to y−4=3(x−8), with a y-intercept of 6, the slope of the given line needs to be determined. The slope of the perpendicular line will be the negative reciprocal of the given slope, and the equation of the line will have the form y = (-1/3)x + 6.
Step-by-step explanation:
To find the equation of a line that is perpendicular to y−4=3(x−8) and has a y-intercept of 6, we need to determine the slope of the given line. The slope of a line written in the form y = mx + b is represented by the coefficient of x, which in this case is 3. Since the line we are looking for is perpendicular, the slope of the perpendicular line will be the negative reciprocal of 3, which is -1/3.
So, the equation of the line perpendicular to y−4=3(x−8) with a y-intercept of 6 will have the form y = (-1/3)x + 6.