To find the equation of a line that passes through the point (7, 3) and is parallel to the line y = x + 3.1, we first need to determine the slope of the given line y = x + 3.1.
In the equation y = mx + b, where m is the slope, the slope of the line y = x + 3.1 is 1. This is because the coefficient of x (which is 1) represents the slope in this form.
Since the line we are looking for is parallel to y = x + 3.1, it will have the same slope as 1.
Therefore, the equation of the line parallel to y = x + 3.1 and passing through the point (7, 3) will have a slope of 1 and will go through the point (7, 3).
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the point (7, 3) and m is the slope (1), we can substitute these values into the formula to find the equation of the line:
y - 3 = 1(x - 7)
y - 3 = x - 7
y = x - 4
Therefore, the equation of the line that passes through the point (7, 3) and is parallel to y = x + 3.1 is y = x - 4.
