Final answer:
To find an equation that is parallel to the line passing through (2,6) and (7,3), we first need to find the slope of the given line. Any equation that has the same slope as the given line will be parallel to it. The equation y = 2x - 2 has a slope of 2, which is parallel to the given line.
Step-by-step explanation:
To find an equation that is parallel to the line passing through (2,6) and (7,3), we first need to find the slope of the given line. The slope of a line can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
Using the coordinates (2,6) and (7,3), we substitute the values into the formula:
slope = (3 - 6) / (7 - 2)
slope = -3/5
Since parallel lines have the same slope, any equation that has a slope of -3/5 will be parallel to the given line. Among the options provided, the equation y = -2x + 4 has a slope of -2, which is different from the slope of the given line. Therefore, the correct equation is y = 2x - 2.