Question

What is an equation of the line that passes through the point left bracket, 2, comma, 6, right bracket(2,6) and is parallel to the line x, minus, y, equals, 2x−y=2?

Answer 1

To find the equation of a line parallel to the given line, we need to determine the slope of the given line. The equation x - y = 2 can be rewritten as y = x - 2.

The slope of this line is 1.

Since the line we are looking for is parallel, it will have the same slope.

Using the point-slope form of a line, we can plug in the values of the given point (2,6) and the slope (1) to find the equation of the line:

y - y1 = m(x - x1)
y - 6 = 1(x - 2)
y - 6 = x - 2
y = x + 4

So, the equation of the line that passes through the point (2,6) and is parallel to x - y = 2 is y = x + 4.