Answer:
y = (-1/5)x + b
Explanation:
The given line is y = 5x. To find a line perpendicular to it, we need to use the fact that the slopes of perpendicular lines are negative reciprocals of each other.
The slope of the given line y = 5x is 5, so the slope of the line perpendicular to it is -1/5.
Let (x1, y1) be any point on the line L. Then the point-slope form of the equation of L is:
y - y1 = m(x - x1)
where m is the slope of the line, which in this case is -1/5.
So the equation of line L in point-slope form is:
y - y1 = (-1/5)(x - x1)
To find the equation of line L in slope-intercept form, we need to solve the point-slope equation for y. First, we can simplify the equation to:
y = (-1/5)x + (1/5)x1 + y1
This equation can be rearranged to the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. In this case:
m = -1/5
b = (1/5)x1 + y1
Therefore, the equation of line L in slope-intercept form is:
y = (-1/5)x + b, where b = (1/5)x1 + y1.