Parallel Lines
Parallel lines are coplanar lines that do not intersect. In two dimensions, parallel lines have the same slope.
The slope m of a line passing through two points (x1 , y1) and (x2 , y2) is:
We can write the equation of a line parallel to a given line if we know a point on the line and an equation of the given line.
Example:
Write the equation of a line that passes through the point (3, 1) and is parallel to the line
y = 2x + 3.
Parallel lines have the same slope.
The slope of the line with equation y = 2x + 3 is 2. So, any line parallel to y = 2x + 3 has the same slope 2.
Now use the slope-intercept form to find the equation.
We have to find the equation of the line which has slope 2 and passes through the point (3, 1). So, replace m with 2, x1 with 3, and y1 with 1.
Use the distributive property.
Add 1 to each side.
Therefore, the line y = 2x – 5 is parallel to the line y = 2x + 3 and passes through the point (3, 1).
