Question

What is the equation of a line through point (0,5) that is parallel to the line with equation y = x - 7?

A) y = x + 5
B) y = x - 2
C) y = x - 7
D) y = x + 7

Answer 1

The equation of the line through point (0,5) that is parallel to the line y = x - 7 is y = x.

Step-by-step explanation:

To find the equation of a line parallel to another line, we need to use the same slope. The given line has a slope of 1, so the parallel line will also have a slope of 1. Since the parallel line passes through the point (0,5) and has a slope of 1, we can use the point-slope form of a line: y - y1 = m(x - x1). Plugging in the values, we get y - 5 = 1(x - 0), which simplifies to y - 5 = x. Therefore, the equation of the line through point (0,5) that is parallel to the line y = x - 7 is y = x (option A).