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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baxthum8's profile pic

baxthum8 | High School Teacher | (Level 3) Associate Educator

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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.

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

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

The slope of your given line is 1. Parallel lines have the same slope. Plug this into the point slope formula and get: 

y - 2 = 1(x - 1)

which is simply 

y - 2 = x -1

and if you're feeling up for it:

y = x + 1 

which is slope intercept form. 

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