Final answer:
The equation of the line perpendicular to y = 8x + 13 with a y-intercept at (0, 10) is y = -1/8x + 10.
Step-by-step explanation:
To write the equation of a line that is perpendicular to another line, we first need to determine the slope of that line. The given line is y = 8x + 13, which has a slope of 8, given by the coefficient of x. For a line to be perpendicular to another, its slope must be the negative reciprocal of the original line's slope. Therefore, the slope of the line we need to find is -1/8 because -1/8 is the negative reciprocal of 8.
Next, we need to include the y-intercept, which is the point where the line crosses the y-axis. The requested y-intercept is (0, 10). Thus, b is 10 in the slope-intercept form of a line, which is y = mx + b where m is the slope and b is the y-intercept.
Combining the slope and y-intercept, the equation of the line perpendicular to y = 8x + 13 with a y-intercept at (0, 10) is y = -1/8x + 10.