# How To Solve (2,-7),y=x-2?

You have not said what solution you seek.

A parallel line through the point will have the same slope, but a different intercept. The new intercept (b') will satisfy the equation
y = x + b'
-7 = 2 + b'    substitute the values at the given point
-9 = b'    subtract 2
Your equation is  y = x - 9.

A perpendicular line through the point will have a slope (m') that is the negative inverse of the slope of your line, which is 1.
-1/1 = m' = -1
So the perpendicular line will have the form
y = -x + b'    where b' is the intercept that makes the line go through the given point
-7 = -(2) + b'    substitute the values at the given point
Your equation is  y = -x - 5.

The distance from the point to the line is
d = |y - x + 2|/√(1^2 + (-1)^2) = |-7 - 2 + 2|/√2 = (7/2)√2
thanked the writer.
It is very easy to solve the above question. You can use the point slope formula for solving this question. You need to understand that if a line is parallel to another line they would have the same slopes.
(2,-7),
y=x-2
Thus slope of the line = m= 1
Using the point slope form

y – y1 = m(x – x1)
Here x1 =2

y1  = -7
then
y-(-7)=1(x-2)
y+7=x-2
y=x-2-7
y=x-9 is the required equation.
thanked the writer. 