Final answer:
The equation of a line parallel to y = 3x - 4 passing through (4,1) is found by using the same slope of 3. By plugging the slope and point into the slope-intercept form, we solve for the y-intercept to obtain the equation y = 3x - 11.
Step-by-step explanation:
To write the equation of a line that is parallel to another line and passes through a given point, one must use the concept of slope. Since parallel lines have the same slope, the line parallel to y = 3x - 4 will also have a slope of 3. Given the point (4,1) through which the new line must pass, the slope-intercept form of the equation of a line y = mx + b can be used, where m is the slope and b is the y-intercept.
Using the slope of 3 and the point (4,1), we can substitute these values into the slope-intercept equation to find the y-intercept (b). The calculation steps are as follows:
- Start with the equation in slope-intercept form: y = mx + b.
- Plug in the slope (3) and the coordinates of the given point, (4,1), resulting in 1 = 3(4) + b.
- Solve for b: 1 = 12 + b gives b = 1 - 12, so b = -11.
Therefore, the equation of the line parallel to y = 3x - 4 and passing through the point (4,1) is y = 3x - 11.