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Two lines are parallel if they have the same slope.
First we need to find the slope m of the line with equation y - x = 6. So,
y - x = 6 add x to both sides to turn the equation into the slope-intercept form
y = x + 6
We know that the slope is the coefficient of the variable x, so the slope is 1. So the line that passes through (5,0) and parallel to the given line has also slope 1.
Using the point (5, 0) = (x1, y1) and m = 1, we write the point-slope form of the equation of the required line,
(y - y1) = m(x - x1) substitute the known values
(y - 0) = 1(x - 5)
y = x + 5 subtract x to both sides to turn this equation into the general form
y - x = 5
Thus, the line that passes through (5,0) and parallel to the given line has the equation
y - x = 5.
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