Answer:
To find the equation of a line perpendicular to y = (2/7)x - 5 and passing through the point (12,12), we can use the fact that the slopes of two perpendicular lines are negative reciprocals of each other.
First, find the slope of the given line by identifying the coefficient of x. In this case, the slope is 2/7.
The negative reciprocal of 2/7 is -7/2. This is the slope of the line we are looking for.
Use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values we have:
y - 12 = (-7/2)(x - 12)
Simplify and rewrite in slope-intercept form (y = mx + b) if desired:
y - 12 = (-7/2)x + 42
y = (-7/2)x + 54
So the equation of the line perpendicular to y = (2/7)x - 5 and passing through the point (12,12) is y = (-7/2)x + 54, which is option 4.
Hope This Helps!