To find the point-slope form of a line that is perpendicular to another line, we first need to determine the slope of the given line.
The equation given is y = 3x. This is in the slope-intercept form (y = mx + b), where m represents the slope. From this equation, we can see that the slope of the line y = 3x is 3.
To find a line that is perpendicular to this one, we need to use the property that the slopes of two perpendicular lines are negative reciprocals of each other. Therefore, if the slope of the given line is 3, the slope of the line that will be perpendicular to it is:
- Perpendicular slope = -1/3
Now, we have the slope of the new line (-1/3) and a point through which it passes, which is (2, 12). We can now use the point-slope form of a line, which is defined as:
y – y1 = m(x – x1)
In this formula:
- (x1, y1) is the point you have, which is (2, 12).
- m is the slope of the line.
Substituting the values into the point-slope form, we get:
y – 12 = -1/3(x – 2)
This equation represents the line in point-slope form that passes through the point (2, 12) and is perpendicular to the line y = 3x.