Final answer:
To find the equation of a line parallel to x - y = 3 and passing through (2, 5), use the slope of the original line (m=1) and apply it to the point-slope formula to get y = x + 3.
Step-by-step explanation:
The equation of a line that is parallel to another can be found by using the same slope as the original line. Since the given line is x - y = 3, we first convert this to slope-intercept form to find its slope. By rearranging the equation, we get y = x - 3, which is the same as y = 1x - 3, where the slope m = 1 and the y-intercept b = -3. A parallel line will have the same slope, so the new line will also have a slope of 1.
To find the equation of the line passing through the point (2, 5), we use the point-slope form of the equation, which is y - y1 = m(x - x1), where (x1, y1) is the point the line goes through and m is the slope. Substituting the given point and slope, we get y - 5 = 1(x - 2), which simplifies to y = x + 3.