what is an equation of the line that passes through the point (2,6) and is parallel to the line x - y = 2?

Explanation:

Step1: Find the slope of the given line

Transform the line $x - y=2$ into slope - intercept form $y = x - 2$. Its slope $m = 1$. Parallel lines have the same slope, so the slope of the required line is also $m = 1$.

Step2: Use the point - slope form to find the equation of the line

The point - slope form is $y - y_1=m(x - x_1)$. Substitute $x_1 = 2,y_1 = 6,m = 1$ into it, we get $y - 6=1\times(x - 2)$.

Step3: Simplify the equation

$y-6=x - 2$, which simplifies to $x - y+4 = 0$.

Answer:

$x - y+4 = 0$