What is the equation of a line parallel to the line x - y = 4 and that passes through the point (1, 2)

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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.

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The equation of a line parallel to x - y = 4 and passing through (1, 2) has to be determined.

The slope of parallel lines is equal.

x - y = 4

=> y = x + 4

The slope of this line is 1.

As the required line passes through (1, 2)

`(y - 2)/(x - 1) = 1`

=> y - 2 = x - 1

=> x - y + 1 = 0

The equation of a line parallel to the line x - y = 4 and passing through the point (1, 2) is x - y + 1 = 0

Approved by eNotes Editorial Team

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