Answer:
y = -6x + 18 is y = 1/6x - 5 in slope-intercept form.
Explanation:
o find the equation of a line perpendicular to another line, we need to determine the negative reciprocal of the slope of the given line.
The given line has a slope of -6. The negative reciprocal of -6 is 1/6. Therefore, the slope of the line we are looking for is 1/6.
Now, we have the slope (m) and one point (6, -4) through which the line passes. We can use the point-slope form of the equation to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is the given point, and m is the slope.
Substituting the values, we have:
y - (-4) = 1/6(x - 6)
Simplifying:
y + 4 = 1/6x - 1
y = 1/6x - 1 - 4
y = 1/6x - 5
Therefore, the equation of the line passing through (6, -4) and perpendicular to y = -6x + 18 is y = 1/6x - 5 in slope-intercept form.