To find the point-slope form of a line that passes through a specific point and is parallel to another line, we first need to understand the slope of the line we are parallel to.
The given line is defined by the equation y = 3x. From this equation, we can directly identify the slope (m) of the line, which is 3.
Since parallel lines share the same slope, the line we want to define will also have a slope of 3. Next, we will use the point-slope form of a line, which is expressed as:
y - y_1 = m(x - x_1)
In this formula:
- (x_1, y_1) is the point the line passes through, and in our case, it is (2, 12).
- m is the slope of the line, which we identified as 3.
Now, we substitute these values into the point-slope form:
y - 12 = 3(x - 2)
This equation represents the point-slope form of the line passing through the point (2, 12) and parallel to the line y = 3x.
Finally, we can rearrange this into slope-intercept form if needed:
y - 12 = 3x - 6
y = 3x + 6
So, the point-slope form of the line is y – 12 = 3(x – 2), and the slope-intercept form is y = 3x + 6.