# Equation of the lineI don't know how to determine the equation of a line wich passes through a point and its parallel to another line . Please give an example.

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### 2 Answers

Given a point on the line and a parallel line is enough information to determine the equation of the line.

The equation of the line is:

y-y1 = m (x-x1)

We are given the point passes through the line (x1, y1) then we can substitute into the equation.

Now to detrmine the slop (m) we look at the parallel line.

the slope of any parallel lines are equal.

For example.

The line passes through ( 1,2) and parallel to y= 3x-2

y-y1- m (x-x1)

==> y-2 = m(x-1)

Now the slope should be equal to the slope of the line y= 3x -2

The slope then is m= 3

==> y-2 = 3 (x-1)

==> y-2 = 3x -3

**==> y= 3x -1**

The equation of a line that passes through a given point A(x0,y0) and it's parallel to a given line: ax + by +c = 0, is:

(x-x0)/-b=(y-y0)/a

We'll work on the following example. The point is (1,1) and the line is 2x-y=8.

We'll make the proper substitutions with the known elements, and the result will be:

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

We'll cross multiply:

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

We'll remove the brackets:

2x-2=y-1

We'll move all terms to one side:

The equation of the line is:

**2x - y - 1 = 0**