In order to findthe equation of a line that is parallel to the line`x - y = 4` we must first determine the slope of the line because parallel lines have the same slope.
In order to find the slope, rewrite the equation in slope-intercept form, `y = mx + b.`
`x - y = 4`
`-y = -x + 4`
`y = x - 4`
This makes the slope of the line 1.
The line must pass through the point (1, 2) so we can use point slope form `(y - y_(1) = m (x -x_(1)))` to write the equation of the line.
`y - 2 = 1 (x - 1)` If needed to write in slope-intercept form the equation would be:
`y = x - 1 + 2 rArr y = x + 1`
Though many answers are required to be written in standard form `ax + by = c` , so this would be:
`x - y = -1`
The equation of the line that is parallel to x - y = 4 and passes through the point (1, 2) is x - y = -1.