To find the point-slope form of the line that passes through the point (2, 12) and is parallel to the line given by the equation y = 3x, we first need to determine the slope of the line we are interested in.
The line y = 3x has a slope of 3. Since parallel lines have the same slope, our new line will also have a slope of 3.
The point-slope form of a linear equation is given by the formula:
y – y1 = m(x – x1)
Where:
- m is the slope of the line.
- (x1, y1) is a point on the line.
In our case, we have:
- m = 3
- (x1, y1) = (2, 12)
Substituting these values into the point-slope formula gives us:
y – 12 = 3(x – 2)
This is the equation of the line in point-slope form that passes through (2, 12) and is parallel to the line y = 3x.