Question

How do you write an equation of a line given (2,-7) and parallel to y=x-2?

Answer 1

`(y + color(red)(7)) = color(blue)(1)(x - color(red)(2))`

Or

`y = x - 9`

Explanation:

If we want a line parallel to the line in the problem it will have the same slope. The equation given in the problem is already in slope intercept form so we can take the slope for the new equation directly from this equation.

The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

`y = color(red)(1)x - color(blue)(2)`

Therefore the slope is `color(red)(m = 1)`

We can now use the point-slope formula to write the equation of the parallel line:

The point-slope formula states: `(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))`

Where `color(blue)(m)` is the slope and `color(red)(((x_1, y_1)))` is a point the line passes through.

Substituting the information from the problem gives:

`(y - color(red)(-7)) = color(blue)(1)(x - color(red)(2))`

`(y + color(red)(7)) = color(blue)(1)(x - color(red)(2))`

Or, we can solve for `y` to put the equation in slope-intercept form:

`y + color(red)(7) = x - color(red)(2)`

`y + color(red)(7) - 7 = x - color(red)(2) - 7`

`y + 0 = x - 9`

`y = x - 9`