The line is perpendicular to y = 16 x + 5 and passes through the point (1, 6).
Question
The line is perpendicular to y = 16 x + 5 and passes through the point (1, 6).
Solution
The first step is to find the slope of the given line. The equation of the line is in the form y = mx + c, where m is the slope. So, the slope of the given line y = 16x + 5 is 16.
The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. Therefore, the slope of the line perpendicular to y = 16x + 5 is -1/16.
The equation of a line is given by y = mx + c. We know the slope (m) is -1/16 and the line passes through the point (1, 6). We can substitute these values into the equation to find the y-intercept (c).
6 = (-1/16)*1 + c 6 = -1/16 + c c = 6 + 1/16 c = 97/16
Therefore, the equation of the line that is perpendicular to y = 16x + 5 and passes through the point (1, 6) is y = -1/16x + 97/16.
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