Final answer:
To find the equation of the line perpendicular to y=27x and passing through (-3,8), we use the negative reciprocal of the given slope and the point-slope form, resulting in y=-1/27x+8 1/27.
Step-by-step explanation:
The question involves finding the equation of a line that is perpendicular to a given line and also passes through a certain point. First, we determine the slope of the given line, which is the coefficient of x in the equation y=27x. The slope of a line perpendicular to this one would be the negative reciprocal of 27, which is -1/27. Using the slope-intercept form y=mx+b, where m is the slope and b is the y-intercept, we substitute the slope and the point (−3,8) into the equation to find b. After calculation, we get that the equation of the required line is y=-1/27x+8 1/27.