Final answer:
The equation of the line passing through the point (10,1) and parallel to the line y-2=5(x+1) is y = 5x - 49.
Step-by-step explanation:
To find the equation of a line that passes through the point (10,1) and is parallel to the line given by y-2=5(x+1), we first need to understand the concept of parallel lines. Two lines are parallel if they have the same slope. The given equation can be rewritten in slope-intercept form as y = 5x + 7, revealing that the slope of the line is 5. To write the equation of a line that is parallel to it and passes through the point (10,1), we use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope of the line.
Substituting the given point and the slope, we get the equation: y - 1 = 5(x - 10). This can be further simplified to standard form: y = 5x - 49, which represents the required equation of the line.