Final answer:
To find the equation of the line that is perpendicular to y = 5x and passes through the point (6, -7), we use the negative reciprocal of the given slope to find the slope of the perpendicular line. Using the point-slope form, we can write the equation of the line as y = -1/5x - 29/5.
Step-by-step explanation:
To find the equation of the line that is perpendicular to the given line and passes through the given point, we need to determine the slope of the perpendicular line. Since the given line has a slope of 5, the perpendicular line will have a slope that is the negative reciprocal of 5, which is -1/5.
Using the point-slope form of a line equation with the coordinates of the given point (6, -7) and the slope (-1/5), we can write the equation as: y - y1 = m (x - x1), where x1 and y1 are the coordinates of the given point.
Substituting the values, we get y - (-7) = -1/5 (x - 6). Simplifying the equation gives y + 7 = -1/5x + 6/5. Rearranging the equation to slope-intercept form (y = mx + b), we have y = -1/5x - 29/5.