What is the slope-intercept form of the line through point (-18, 5) that is perpendicular to the line y = 3x - 6?

To find the slope-intercept form of the line that is perpendicular to another line, you first need to identify the slope of the given line. The line provided in the question is in slope-intercept form ( y = mx + b ), where ( m ) represents the slope. For the line ( y = 3x - 6 ), the slope ( m ) is 3.

When two lines are perpendicular, their slopes are negative reciprocals of each other. Therefore, to find the slope of the line that is perpendicular to the line ( y = 3x - 6 ), you take the negative reciprocal of 3, which is (-\frac{1}{3}).

Now, you use the point-slope form of a line equation with the slope (-\frac{1}{3}) and the given point (-18, 5). The point-slope form is expressed as:

[

y - y_1 = m(x - x_1)

]

Substituting the known values into this formula, you get:

[

y - 5 = -\frac{1}{3}(x + 18)

]

Next, distribute the (-\frac