Graph the line.
y-1=3(x-4)

Step 1 ：This is a linear equation in point-slope form, \(y - y1 = m(x - x1)\), where m is the slope of the line and \((x1, y1)\) is a point on the line. In this case, the slope m is 3 and the point \((x1, y1)\) is \((4, 1)\).

Step 2 ：To graph this line, we can start by plotting the point \((4, 1)\) and then use the slope to find other points on the line. The slope 3 means that for each step to the right along the x-axis, we go three steps up along the y-axis.

Step 3 ：The graph of the line \(y - 1 = 3(x - 4)\) is a straight line that passes through the point \((4, 1)\) and has a slope of 3. This means that for every 1 unit increase in x, y increases by 3 units. The line extends infinitely in both the positive and negative directions.

Step 4 ：\(\boxed{\text{The graph of the line } y - 1 = 3(x - 4) \text{ is a straight line that passes through the point } (4, 1) \text{ and has a slope of 3.}}\)